AP Physics B Kinematics Presentation #38

The New Jersey Center for Teaching and Learning
26 Jun 201210:00
EducationalLearning
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TLDRThe video script explains the physics behind a boy throwing a ball vertically upwards and catching it after 3 seconds. It covers the concept of projectile motion, the effect of gravity with an acceleration of 9.8 m/s², and the symmetry of time for ascent and descent. Two methods are presented to calculate the maximum height reached by the ball, resulting in approximately 11 meters. The first method involves solving for initial velocity and using kinematic equations, while the second simplifies the process by focusing on the falling phase and the equation of motion.

Takeaways
  • 🏐 The boy throws a ball vertically upwards and catches it after 3 seconds.
  • ⏱ The total time for the ball's trajectory is 3 seconds, with equal time for ascent and descent (1.5 seconds each).
  • 📉 The acceleration acting on the ball is due to gravity, which is 9.8 m/s².
  • 🔍 The initial and final velocities are unknown, requiring inference for calculation.
  • 🔑 The first method involves using kinematic equations to solve for the initial velocity and height.
  • 🔢 The initial velocity is calculated to be 14.7 m/s using the equation v = v₀ - gt.
  • 📈 The height reached by the ball is then calculated using the equation y = v₀t - 1/2gt².
  • 📉 The second method simplifies the problem by considering the ball's fall and using the equation y = 1/2gt².
  • 📋 Both methods yield a height of approximately 11 meters, rounded to significant figures.
  • 📝 The importance of considering significant figures in scientific calculations is highlighted.
  • 📚 The script provides a detailed explanation of two methods to solve the problem, emphasizing the process and the thought behind each step.
Q & A

  • What is the total time of the ball's trajectory described in the script?

    -The total time of the ball's trajectory is 3 seconds.

  • What is the acceleration acting on the ball during its trajectory?

    -The acceleration acting on the ball is due to gravity, which is 9.8 m/s².

  • How is the total time of 3 seconds divided between the ascent and descent of the ball?

    -The time up and the time down are the same, each being 1.5 seconds.

  • What is the initial velocity of the ball when it is thrown upwards?

    -The initial velocity is calculated to be 14.7 m/s, which is derived from the time and acceleration.

  • How is the height the ball reaches calculated in the script?

    -The height is calculated using the kinematic equations, considering the initial velocity and acceleration due to gravity.

  • What is the significance of the initial velocity in solving for the height reached by the ball?

    -The initial velocity is crucial as it, along with the time and acceleration, determines the maximum height the ball reaches.

  • Why are two methods presented for calculating the height reached by the ball?

    -Two methods are presented to provide alternative approaches, one being more involved and the other being simpler and more elegant.

  • What is the height the ball reaches according to the calculations in the script?

    -The height the ball reaches is approximately 11 meters, rounded to three significant figures.

  • Why is the second method considered simpler and more elegant than the first?

    -The second method is simpler because it reduces the problem to a single equation involving only acceleration and time, which are known quantities.

  • How does the script handle the significant figures in the final height calculation?

    -The script rounds the height to three significant figures, resulting in 11.0 meters, omitting the trailing zero.

  • What is the importance of considering both the ascent and descent in the script's explanation?

    -Considering both the ascent and descent helps to understand the entire trajectory and provides insights into different aspects of the motion.

Outlines
00:00
🚀 Calculating the Maximum Height of a Vertically Thrown Ball

The script begins with a physics problem involving a boy who throws a ball vertically upwards and catches it after 3 seconds. It's established that the total time of the ball's trajectory is 3 seconds, and the acceleration due to gravity is 9.8 m/s². The script explains that the time taken for the ball to ascend and descend is equal, each being 1.5 seconds. The first method to calculate the height involves using the kinematic equations to solve for the initial velocity (14.7 m/s) and then using this to find the height reached by the ball, which is approximately 11 meters. The second method simplifies the process by focusing on the descent, using the same kinematic equations but with the final position set to zero, leading to the same result of 11 meters for the height reached.

05:02
📚 Two Methods to Determine the Height Reached by a Thrown Ball

The second paragraph elaborates on two methods to calculate the height a ball reaches when thrown vertically upwards. The first method involves complex calculations using the initial velocity found from the ascent phase, leading to a height of 11 meters. The second method is more straightforward, using the descent phase and simplifying the kinematic equation to solve for height, also resulting in 11 meters. The paragraph emphasizes the importance of understanding both methods, as they provide insight into different aspects of the problem, such as the initial velocity of the throw and the height reached by the ball.

Mindmap
Keywords
💡Vertical throw
Vertical throw refers to the act of propelling an object upward against gravity, in this case, a ball. It is central to the video's theme as it is the primary action performed by the boy. The script describes the boy throwing the ball upwards and catching it after it falls back down due to gravity, illustrating the concept of vertical throw.
💡Trajectory
Trajectory is the path that an object follows through space as a result of its motion. In the video script, the trajectory is the path of the ball as it is thrown upwards and falls back down. The concept is used to explain the physics of the ball's motion and to calculate the height it reaches.
💡Acceleration due to gravity
Acceleration due to gravity is the rate at which an object's velocity changes due to the force of gravity. The script mentions 9.8 m/s² as the acceleration acting on the ball, which is a constant value representing the acceleration due to gravity near the Earth's surface. It is a key factor in determining the height the ball reaches.
💡Projectile motion
Projectile motion is the motion of an object thrown or projected into the air, influenced only by the force of gravity. The script discusses the ball's motion as an example of projectile motion, with the time taken to go up and come down being equal, which is a characteristic of this type of motion.
💡Time up and time down
Time up and time down refer to the duration it takes for the ball to reach its highest point and the duration it takes to fall back down to the starting point, respectively. The script uses these terms to explain that the total time of the ball's flight is divided equally between the ascent and descent, which is 1.5 seconds each in this case.
💡Initial velocity
Initial velocity is the speed at which an object starts moving. The script calculates the initial velocity of the ball by using the time it takes to reach the apex and the acceleration due to gravity, which is essential for determining the height the ball reaches.
💡Kinematic equations
Kinematic equations are formulas used to describe the motion of an object when forces are acting upon it. The script references these equations to solve for the height the ball reaches and the initial velocity, showing how they are applied in the context of the ball's vertical throw.
💡Significant figures
Significant figures are the digits in a number that carry meaning contributing to its precision. The script mentions rounding the calculated height to three significant figures, which is an important concept in scientific calculations to ensure accuracy and precision.
💡Apex
Apex refers to the highest point reached by an object in its trajectory. In the script, the apex is the point at which the ball's velocity becomes zero before it starts falling back down, and it is used to calculate the initial velocity of the ball.
💡Height
Height, in the context of the script, is the maximum vertical distance the ball travels from the point of release to the apex. The script calculates this height using the kinematic equations and the known values of time and acceleration due to gravity.
💡Method
Method refers to the approach or technique used to solve a problem. The script presents two methods for calculating the height the ball reaches, one involving solving for the initial velocity and the other simplifying the kinematic equation to involve only time and acceleration.
Highlights

A boy throws a ball vertically upwards and catches it after 3 seconds, prompting the question of how high the ball reached.

The entire trajectory of the ball's motion lasts for 3 seconds.

The acceleration acting on the ball is due to gravity, at 9.8 m/s squared.

The time taken for the ball to go up and come back down is the same, each being 1.5 seconds.

Two methods are presented to solve for the height the ball reaches in its trajectory.

The first method involves using the kinematic equations to solve for velocity and height.

The second, simpler method reduces the problem to an equation involving only acceleration and time.

The initial velocity of the ball is calculated to be 14.7 m/s using the first method.

Using the first method, the height reached by the ball is calculated to be approximately 11 meters.

Significant figures are considered in the calculations, rounding the height to 11 meters.

The second method provides a more elegant solution by focusing on the falling part of the trajectory.

By considering the falling part, the equation simplifies to only terms of acceleration and time.

The height reached by the ball is also calculated to be 11 meters using the second method.

Both methods yield the same result, validating the solution.

The problem-solving approach demonstrates the application of physics principles to real-world scenarios.

The transcript provides a step-by-step explanation of the problem-solving process.

The solution to the problem involves understanding projectile motion and the effects of gravity.

The transcript concludes by emphasizing that either method can be used to find the height the ball reaches.

Transcripts

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PhysicsProjectile MotionVertical ThrowBall CatchGravityTime CalculationHeight FormulaMotion AnalysisEducational ContentScience Experiment