The collection of exercises, often formatted as a handout or digital document, focuses on applying physics principles to scenarios involving objects accelerating solely under the influence of gravity. These resources typically present a series of quantitative challenges where learners must calculate variables such as final velocity, displacement, and time, given initial conditions. For example, a typical question might involve determining the impact speed of an object dropped from a specific height, neglecting air resistance.
These educational tools play a critical role in solidifying understanding of kinematics and Newtonian mechanics. By working through diverse problem sets, students develop analytical skills necessary for solving real-world physics issues. Historically, such problem sets have been a cornerstone of physics education, evolving from textbook examples to interactive simulations and online resources, reflecting advancements in pedagogical techniques and technology.
Further exploration of these resources reveals varying levels of complexity, catering to different stages of learning. The selection of appropriate problems allows educators to tailor instruction, reinforcing fundamental concepts while gradually introducing more challenging applications of gravitational acceleration.
1. Acceleration due to gravity
The story begins with a fundamental truth: an object released in a vacuum accelerates downwards. This acceleration, approximately 9.8 meters per second squared on Earth, is the cornerstone of understanding free fall. A direct consequence of this consistent downward pull is the ability to predict and calculate the motion of falling bodies. The exercises designed around this concept offer a structured approach to mastering the physics involved. A projectile launched upwards will decelerate due to gravity until it reaches its apex, then accelerate downwards. The problem sets demand a quantifiable grasp of this entire trajectory, illustrating the direct effect of this fundamental acceleration. Ignoring this inherent acceleration within those exercises makes them unsolvable.
Consider the design of bridges or the trajectory calculations for artillery: both rely on precise knowledge of gravitational effects. These worksheets represent a simplified, yet vital, step in acquiring such expertise. By methodically working through variations, one learns to extract meaningful data from given parameters, manipulate kinematic equations, and interpret results within a real-world context. For instance, calculating the drop time for a package released from an aircraft requires accurate application of the constant acceleration formula, where gravitational pull is the driving force. Without understanding and accurately applying its value, the package might miss its intended target by a significant margin.
In essence, problem sets designed around free fall represent applied lessons in harnessing the implications of a consistent natural phenomenon. The exercises offered serve to solidify comprehension, demonstrate the predictive power of physics, and highlight the real-world significance of mastering fundamental principles. By systematically addressing challenges, learners develop both analytical skills and a deeper appreciation for the pervasive influence of gravitational acceleration.
2. Initial velocity considerations
The descent of an object isnt always a simple drop from rest. Often, it’s propelled into motion, either upwards or downwards, before the unrelenting force of gravity takes command. This initial impetus, the velocity imparted at the start, significantly shapes the object’s trajectory and is a critical component in any calculations related to gravitational acceleration. The challenges within the resources focusing on gravitational acceleration commonly hinge on understanding how to incorporate this factor into relevant equations.
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Upward Trajectory Calculations
An object projected skyward begins its journey against gravity. The exercises often require determining the maximum height reached or the total time spent aloft. Accurate assessment involves factoring in the initial upward speed, which gradually diminishes until the object momentarily pauses at its peak before succumbing to downward acceleration. The complexity arises in understanding the symmetry of this motion: ascent time equaling the time for descent, assuming the object returns to the same starting level.
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Downward Launch Velocity
Consider a stone thrown vertically downwards from a bridge. The initial downward velocity adds directly to the effect of gravity, increasing the rate at which speed accumulates. Problems of this nature necessitate recognizing that the object is already in motion, distinguishing them from simple scenarios where the object starts from a standstill. Students must carefully sum the effects of initial speed and gravitational acceleration to accurately predict impact velocity.
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Horizontal Projectile Motion
The introduction of horizontal motion adds a layer of complexity. An object launched horizontally, like a ball rolled off a table, experiences both horizontal and vertical movements independently. While gravity dictates the vertical descent, the initial horizontal speed remains constant (assuming negligible air resistance). Combining these two independent motions allows prediction of the projectile’s range and impact point. Problem sets demand dissecting the motion into components, applying appropriate formulas to each, and then synthesizing the results to paint a complete picture.
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Angled Projection Problems
The most intricate scenarios involve objects launched at an angle to the horizontal. Resolving the initial velocity into vertical and horizontal components becomes crucial. The vertical component determines the object’s height and flight time, while the horizontal element governs its range. These problems require application of trigonometric functions to accurately separate the initial speed into its constituent parts, setting the stage for subsequent calculations. Incorrect resolution leads to significant errors in determining range, maximum height, and flight duration.
These considerations form the backbone of understanding motion under gravitational influence, going beyond simple drops to encompass a multitude of real-world scenarios. Ignoring this information within the exercises compromises the entire analytical process. By mastering the incorporation of this crucial factor, learners develop a nuanced understanding of how gravitational force interacts with motion, setting the stage for advanced applications in physics and engineering.
3. Displacement calculations
At the heart of every challenge related to gravitational physics lies a single, crucial question: How far? The pursuit of this answer manifests as a critical need for meticulous displacement calculations. These calculations are not merely academic exercises but rather narratives of motion, tracing the path an object carves through space and time under the relentless pull of Earth. Within the context of those resources, these are the bedrock upon which understanding is built.
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Initial Height and Reference Points
Every scenario begins with a starting point, a reference against which all subsequent movement is measured. Determining the initial height is paramount because it anchors the calculation, establishing the potential energy the object possesses before its fall. A mistake here ripples through the entire problem, distorting the final answer. Consider a construction worker dropping a tool from a scaffolding; the height of the scaffolding dictates the potential energy and, therefore, the subsequent impact velocity. The problems presented force a careful consideration of this initial condition, emphasizing its real-world consequences.
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Accounting for Direction
Displacement is not merely distance; it is distance with direction. In gravitational problems, direction is inherently tied to the pull of gravity, typically downwards. However, if an object is thrown upwards, the initial displacement is positive, against gravity, until it reaches its apex. A lack of attention to this detail, a failure to properly assign positive and negative signs, renders the calculation meaningless. The exercises demand that learners constantly evaluate the direction of motion, reinforcing the concept of displacement as a vector quantity. Imagine a projectile launched from a cliff; its displacement will first be positive (upwards), then negative (downwards) relative to the cliff top, a detail vital for calculating its final position.
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The Constant Acceleration Equation
The tool most frequently employed in finding displacement is the constant acceleration equation. This equation elegantly relates initial velocity, time, acceleration (gravity, in this case), and displacement. Mastering its application is key to solving the exercises. However, rote memorization is insufficient; understanding the physical meaning of each term is crucial. A common mistake involves using the wrong sign for acceleration or failing to convert units properly. The exercises serve as a proving ground, where understanding of the equation is tested through diverse and challenging scenarios. For example, determining the depth of a well by timing a dropped stone requires precise application of the constant acceleration equation, accounting for both the time it takes the sound to return and its relation with distance traveled.
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Relating Displacement to Other Variables
Displacement doesn’t exist in isolation; it is intrinsically linked to velocity and time. The problems often require using other kinematic equations to first determine these variables before calculating displacement. For instance, finding the final velocity of an object dropped from a height allows calculation of displacement over a given time interval. The interconnection of these concepts underscores the holistic nature of physics. The exercises encourage critical thinking, forcing the integration of multiple equations to solve complex scenarios. Calculating the landing point of a ski jumper requires relating initial velocity, launch angle, air time, and gravitational acceleration to determine the total displacement, demonstrating the interconnectedness of all kinematic variables.
In essence, mastering displacement calculations in gravitational scenarios is not merely about plugging numbers into formulas; it’s about understanding the interplay of motion, direction, and time. The exercises encourage a deep engagement with these concepts, fostering analytical and problem-solving skills applicable far beyond the confines of the classroom. They serve as a reminder that physics is not a collection of abstract equations but a language for describing the universe in motion.
4. Time-dependent motion
The narrative of any falling object is inextricably linked to the passage of time. Each second marks a new chapter in its descent, a quantifiable increase in velocity dictated by the unyielding pull of gravity. The “free fall problems worksheet” serves as a chronicle of this temporal progression, demanding a precise understanding of how displacement and velocity evolve with each passing moment. Neglecting the time element in these calculations is akin to omitting a vital character from the story, rendering the plot incomprehensible. The worksheets present scenarios that unfold as clock ticks by, where objects accelerate at a constant rate, illustrating how initial conditions cascade through time to determine the final outcome. For instance, a stone dropped into a well presents a classic example. The time it takes for the stone to hit the bottom directly relates to the depth of the well, a spatial dimension revealed through the temporal duration of its descent.
Consider also the arc of a projectile launched into the air. The “free fall problems worksheet” might ask for the total time of flight or the time to reach maximum height. Solving these problems requires meticulously accounting for the influence of gravity over time, separating the trajectory into ascent and descent phases, each governed by the same constant acceleration but acting in opposite directions. The temporal aspect is not merely a variable to be plugged into an equation but the very fabric upon which the story of the projectile’s motion is woven. A pilot calculating the drop point for supplies needs to understand how wind resistance and gravity will affect the package over time. A delay of even a second could cause the package to miss the target. Such temporal awareness transforms physics from abstract theory into practical necessity.
Ultimately, understanding motion under gravity involves grasping the intimate dance between displacement, velocity, and the relentless march of time. The exercises challenge students to dissect motion into discrete temporal segments, to apply kinematic equations with precision, and to interpret the results within a temporal framework. These worksheets are not just about finding the right answer; they are about understanding the story of motion as it unfolds through time, a narrative where gravity dictates the tempo, and time measures the falling object’s journey.
5. Neglecting air resistance
The realm of idealized gravitational acceleration opens when the story omits a persistent character: air resistance. Problem sets exploring these concepts often state, as a silent agreement, that air resistance is negligible. This isn’t a mere oversight; it’s a purposeful simplification. Its absence transforms the problem from a complex, real-world scenario into a more accessible, solvable equation. Imagine a feather and a stone dropped simultaneously. In reality, the feather flutters, its descent a slow dance with air currents, while the stone plummets. But in the world of the simplified worksheets, both accelerate at the same rate, pulled only by gravity, their size and shape rendered irrelevant.
This exclusion allows a focus on the core principles of kinematics: constant acceleration, predictable trajectories, and the elegant relationships between displacement, velocity, and time. By setting aside the complexities of fluid dynamics, the underlying physics become clearer. Students can master the manipulation of equations, the interpretation of graphs, and the prediction of outcomes. The lessons prepare a bedrock of understanding upon which more intricate models can later be built. Consider a skydiver: initially, air resistance is minimal, and the acceleration is close to the idealized value. However, as speed increases, air resistance becomes significant, eventually reaching a point where acceleration ceases, and the skydiver falls at a constant speed. The worksheets capture that initial phase, the moment before reality intervenes. Similarly, for projectiles such as bullets, accounting for air resistance becomes crucial, but initial calculations benefit from simplified models.
The assumption of negligible air resistance serves as a pedagogical bridge. It offers an accessible introduction to complex physical phenomena. While it sacrifices realism, it fosters a solid understanding of fundamental principles. The exercises provided showcase a world where gravity reigns supreme, unburdened by the complexities of atmosphere, allowing students to grasp the core mechanics of free fall before venturing into more complex, real-world scenarios. Acknowledging this simplification is the cornerstone of learning, and mastering the basics before delving into the complexities of the real world.
6. Final velocity determination
The denouement of every free fall scenario rests upon a single, decisive value: the final velocity. It is the culmination of gravity’s relentless acceleration, the ultimate speed an object attains before impact or the termination of its descent. Within the confines of a “free fall problems worksheet,” the final velocity serves not just as an answer, but as a testament to the correct application of kinematic principles. It is the tangible result of untangling the intricate relationships between initial conditions, time, and acceleration. The problems presented become more than just exercises; they become quests to unveil the magnitude of this concluding speed.
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Applying Kinematic Equations
The pursuit of final velocity hinges upon the judicious selection and application of kinematic equations. Each equation offers a unique pathway, dependent on the available initial data. When the initial velocity, acceleration, and time are known, a direct calculation ensues. Should displacement and acceleration be provided, a different equation comes into play. This process mirrors the investigative work of a detective, piecing together clues to solve a mystery. The worksheets test this ability, forcing the solver to discern the most efficient route to the final answer. A correct application not only reveals the speed but also validates the entire process.
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Understanding Energy Conservation
Another lens through which final velocity may be viewed is energy conservation. The initial potential energy of an object at height transforms into kinetic energy as it falls. Setting these two energies equal allows direct calculation of the velocity just before impact, bypassing the need for time measurements. This approach offers a more elegant, simplified solution, particularly useful when time is not a given. However, it reinforces the principle that energy is neither created nor destroyed, merely transformed. The problems showcase this principle, linking initial conditions to the ultimate speed through energy equations.
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Considering Direction and Sign Conventions
Final velocity is not merely a magnitude; it is a vector, possessing both magnitude and direction. Establishing a consistent sign convention becomes crucial. Typically, downward motion is assigned a negative sign, reflecting the direction of gravitational acceleration. A failure to adhere to this convention leads to a discrepancy in the final answer, a sign of a misunderstanding of the physics. The exercises force the practitioner to constantly evaluate the direction of motion, reinforcing the vector nature of velocity. The final velocity becomes a declaration of both speed and direction, a complete description of the object’s state.
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Real-World Implications and Safety Factors
The determination of final velocity extends beyond academic exercises. Engineers use these calculations to design structures, assess impact forces, and ensure safety. The final velocity of a falling object dictates the stresses on a material upon impact, guiding material selection and structural design. Similarly, in accident reconstruction, determining the impact velocity of a vehicle is critical for understanding the forces involved and the potential for injury. Those exercises, simplified though they may be, represent the fundamental building blocks for such real-world applications. Understanding the calculations directly translates to designs and practices that could prevent harm.
Thus, within the framework of a “free fall problems worksheet,” the pursuit of final velocity becomes an exercise in applied physics, a journey through equations, and a lesson in the consequences of motion. Each successful calculation reinforces not only the understanding of kinematic principles but also an appreciation for the real-world implications of such analyses. The ultimate speed achieved is not just a number, but a story of gravity’s influence, a testament to the power of physics to predict and understand the world around us.
7. Constant acceleration equation
The constant acceleration equation acts as the central cipher within the domain of gravitational studies. It is the essential tool for unraveling the mysteries presented within “free fall problems worksheet,” serving as the mathematical lens through which motion is quantified and understood. Without this equation, the problems presented would remain insoluble puzzles, their inherent relationships obscured by the complexities of variable motion.
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Displacement as a Function of Time
The equation provides the means to determine how far an object travels under the constant influence of gravity in a given interval. This is the cornerstone of many of the challenges within the resources. Scenarios where one must calculate the height from which an object fell based on the time it takes to reach the ground rely almost exclusively on this relationship. In a practical sense, civil engineers estimating the potential impact zone of debris falling from a building under construction employ this principle, demonstrating the real-world application of this foundational equation.
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Velocity Changes Over Time
Another aspect is its role in determining how quickly the speed of a falling body changes as time elapses. This facet allows precise calculation of impact velocities, a vital consideration in safety engineering and forensic analysis. Exercises demanding the final speed of an object dropped from a specific height directly test understanding of this relationship, revealing how gravitational force compounds over time to create potentially hazardous situations. Understanding of this velocity transformation is essential for calculating energy transfer when an object impacts another object.
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Initial Velocity Considerations
The constant acceleration equation also accounts for situations where an object has an initial velocity, either upward or downward, adding another layer of complexity. Problems that involve calculating the maximum height reached by an object launched upward, or the time it takes to hit the ground when thrown downwards, all require modification to account for the initial speed. Ballistics, for example, relies heavily on modifying and understanding all these equations.
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Interrelation of Variables
The power of the constant acceleration equation lies in its capacity to relate displacement, initial velocity, final velocity, acceleration, and time. Problems often require determining one unknown quantity given several known variables, forcing students to manipulate and rearrange the equation to isolate the desired value. This exercise fosters analytical skills crucial for solving real-world engineering problems, such as calculating the required thrust to slow a descending spacecraft or determining the stopping distance of a vehicle on an incline.
These facets collectively underscore the indispensable role of the constant acceleration equation in understanding and solving “free fall problems worksheet.” It serves as the unifying principle that transforms seemingly disparate exercises into applications of a single, powerful law. By mastering its nuances, students unlock the ability to predict and quantify the motion of objects under the constant influence of gravity, a capability with wide-ranging applications in science and engineering.
8. Kinematic equations application
The “free fall problems worksheet” exists as a direct consequence of kinematic equations application. These equations, born from the principles of classical mechanics, provide the framework to describe motion with constant acceleration, a condition inherent to free fall scenarios. Absent these equations, the worksheet transforms into an unsolvable collection of hypothetical situations. In essence, these equations are the alphabet through which the story of a falling object is told. The initial velocity acts as a catalyst, the displacement reflects the objects path, the time becomes the ticking sound of gravity pull and then final speed comes to its end. For instance, if one wishes to determine the velocity of an object just before it hits the ground, the appropriate kinematic equation provides the answer when furnished with the object’s initial height and gravitational acceleration. Without this equation, such a calculation becomes an impossible task, underscoring the equation’s position.
The utility is not confined to academia alone. Consider engineers designing a restraint system for a rollercoaster. The understanding of forces is tied to the safety of the project. To accurately measure and simulate the dynamic process is fundamental to a successful output. Such system requires an exact simulation to withstand the harsh conditions of constant usage. Similarly, in forensic science, kinematic equations are essential for accident reconstruction. By analyzing skid marks, impact angles, and final resting positions, experts can reverse-engineer events, revealing impact velocities and points of origin. All these calculations depends on Kinematic equations applications.
Mastery in these equations is not merely about formulaic substitution; it demands the ability to dissect scenarios, identify relevant variables, and select the appropriate equation. The “free fall problems worksheet” serves as a training ground for this skill, honing analytical capabilities and providing practical application of theoretical knowledge. Challenges arise when students attempt to apply equations blindly, neglecting considerations such as the direction of velocity and displacement. The ultimate lesson lies not just in finding the right answer, but in understanding the physics of motion. Its is not only a theoretical framework but rather a practical tool used in real-world context.
Frequently Asked Questions about Resources Examining Gravitational Acceleration
Navigating the landscape of physics education requires a clear understanding of the common hurdles and misconceptions that arise. This section addresses frequently encountered questions, providing guidance for both students and educators using these resources.
Question 1: Why do these exercises often ignore air resistance? Isn’t that unrealistic?
The absence of air resistance is a deliberate simplification. Like a painter choosing a minimalist palette, the exercises aim to highlight the core principles of gravitational acceleration. Introducing air resistance would mire the problem in complex fluid dynamics, obscuring the foundational concepts. Think of it as learning to walk before running; mastering idealized motion is essential before tackling real-world complexities.
Question 2: How do I choose the correct kinematic equation for a given problem?
Selecting the appropriate equation is akin to choosing the right key for a lock. Each equation relates different variables, like pieces of a puzzle. Identify what is known and what needs to be found. For instance, if time is absent, use the equation that excludes it. This process demands analytical skill, transforming you from a passive equation user to an active problem solver.
Question 3: What is the significance of the negative sign in gravitational acceleration (-9.8 m/s)?
The negative sign is not a mere detail; it is a directional compass. Like assigning north and south on a map, it establishes a frame of reference. Conventionally, upward motion is positive, making downward acceleration negative. Consistency is paramount; a failure to adhere to sign conventions can lead to errors.
Question 4: How do I account for initial velocity when an object is thrown upwards?
An object launched upward fights gravity’s pull. This initial velocity diminishes as it ascends, ultimately reaching zero at its peak. The challenge is to incorporate this initial impetus into calculations. Like a river flowing against the current, the initial velocity counteracts gravity. Understanding this interaction is crucial for determining maximum height and flight time.
Question 5: What if I am given a problem where the object is launched at an angle?
Angled launches require dissection. Like a prism splitting light, the initial velocity must be resolved into vertical and horizontal components. The vertical component dictates the height and flight time, while the horizontal governs the range. This decomposition demands application of trigonometric functions, transforming a complex motion into manageable parts.
Question 6: Are these exercises applicable to real-world scenarios, given the simplifications?
Despite the simplifications, these exercises are the bedrock of real-world applications. Like learning scales before composing a symphony, they provide the fundamental understanding necessary for more complex analyses. While the exercises may ignore air resistance, they instill an intuitive understanding of gravitational acceleration, a skill applicable in fields ranging from engineering to astrophysics.
These questions and answers represent a compass, guiding you through the learning process. Remember, the aim is not rote memorization, but rather a deep understanding of the underlying physics.
Strategies for Mastery
Like a seasoned explorer charting unknown territories, navigating gravitational challenges demands preparation, insight, and a methodical approach. The challenges found within these exercises are not obstacles, but rather opportunities to solidify understanding of fundamental physical laws. Careful implementation of the tips outlined below can transform confusion into clarity, and lead to successful solutions.
Tip 1: Establish a Consistent Sign Convention: Just as a ship relies on a steadfast compass, the calculations require a consistent sign convention. Designate a direction as positive (usually upwards) and consistently apply this convention to velocity, displacement, and acceleration. This eliminates confusion and prevents errors.
Tip 2: Sketch the Scenario: Before reaching for an equation, visualize the scene. Just as an artist composes a painting, sketching the problem allows grasping of the motion’s dynamics. Label known variables and clearly indicate the direction of movement. This visual aid provides a framework for problem-solving.
Tip 3: Identify Knowns and Unknowns: Like a detective gathering clues, meticulously list all known variables and clearly define what must be determined. Organize the information to streamline the selection of the appropriate kinematic equation.
Tip 4: Select the Appropriate Kinematic Equation: From the array of available formulas, like choosing the proper tool from a kit, select the equation which connects known to unknown. Be deliberate. This choice is crucial for solving the problem at hand.
Tip 5: Pay Attention to Units: Inconsistent units undermine even the most accurate calculations. Like carpenters ensuring a level foundation, always convert all values to a consistent system, preferably meters, seconds, and kilograms.
Tip 6: Consider the Physical Meaning of Results: After obtaining an answer, pause and reflect. Does the result make sense in the context of the problem? If calculating impact velocity, is the value reasonable? This critical thinking reinforces understanding and detects potential errors.
Tip 7: Break Down Complex Problems: Similar to a general dividing forces, complex problems benefit from division into smaller, manageable stages. Consider the ascent and descent phases of projectile motion separately. This simplifies calculations and promotes clarity.
By implementing these strategies, success is more than achievable. Careful preparation, methodical execution, and critical reflection transform the gravitational questions from daunting challenges to opportunities for profound comprehension.
As the journey through dynamics reaches its conclusion, the insights gained from tackling these exercises equip learners with a strong foundation in classical mechanics, essential for success in advanced studies.
The Final Descent
The preceding exploration has navigated the varied terrain encompassed by educational materials dedicated to gravitational acceleration. From foundational kinematic principles to nuanced problem-solving techniques, the journey has illuminated the critical role these resources play in solidifying understanding of classical mechanics. Mastery of the exercises presented within these materials unlocks an ability to predict and quantify the behavior of objects under the influence of gravity, a skill applicable across diverse scientific and engineering disciplines.
The lessons learned should transcend the confines of the classroom. The ability to dissect complex scenarios, identify relevant variables, and apply appropriate equations speaks to a broader capacity for critical thinking and problem-solving. Let the understanding gained serve as a springboard for continued exploration of the physical world, a constant reminder that the universe itself offers the ultimate worksheet, filled with problems waiting to be solved.
