AP Physics 1 Kinematics Free Response 9

Allen Tsao The STEM Coach
15 Nov 201804:57
EducationalLearning
32 Likes 10 Comments

TLDRIn this AP Physics video, Alan explores the minimum initial velocity required for a ball to reach Ted on a separate building. He uses kinematics to break down the problem in the x and y directions, solving for time in the air and the horizontal distance covered. The solution involves understanding projectile motion and the effects of gravity, ultimately finding the answer to be 25 meters per second.

Takeaways
  • 🏙️ The problem involves Bill and Ted on the roofs of two separate buildings separated by a distance D.
  • 🏋️‍♂️ Bill throws a super ball with an initial velocity parallel to the ground.
  • 🚀 The ball is thrown in such a way that it bounces once on the ground before reaching Ted.
  • 🔄 The super ball has a property where its velocity in the X direction remains the same after the bounce, and its Y velocity becomes negative.
  • 📏 The distance between the buildings is given as D, and the height of the buildings is H.
  • 📉 The height H is set to 100 meters, which is beyond Bill's throwing range.
  • 🔍 The goal is to find the minimum initial velocity (V not) required for the ball to just reach Ted.
  • 📚 The problem is approached by analyzing the motion in both the X and Y directions separately.
  • 🔢 In the X direction, the equation D = V not * T is used, where T is the time the ball is in the air.
  • 📉 In the Y direction, the equation H = 0.5 * a * T^2 is used, where a is the acceleration due to gravity (9.8 m/s^2).
  • ⏱️ The time the ball is in the air is determined to be 4 seconds by solving the Y direction equation.
  • 🔑 The minimum initial velocity V not is calculated to be 25 m/s by dividing the distance D (100 meters) by the time T (4 seconds).
Q & A

  • What is the main problem discussed in the video?

    -The main problem discussed in the video is finding the minimum velocity (V not) at which Bill needs to throw a super ball so that it just reaches Ted, after bouncing once on the ground between two buildings.

  • What is the distance between the two buildings where Bill and Ted are located?

    -The distance between the two buildings is D, which is given as 100 meters.

  • What is the height of the buildings from which Bill and Ted are throwing and catching the ball?

    -The height of both buildings is H, which is also given as 100 meters.

  • What is the condition for the ball's velocity when it hits the ground?

    -When the ball hits the ground, its velocity in the X direction remains the same, and its velocity in the Y direction becomes negative V Y.

  • Why is the ball thrown horizontally?

    -The ball is thrown horizontally so that its initial velocity in the Y direction is zero, making the problem easier to solve using projectile motion equations.

  • What is the symmetry in the problem that helps in visualizing the trajectory of the ball?

    -The symmetry in the problem is that the time it takes for the ball to rise and fall is the same, which helps in visualizing the trajectory as halfway down and halfway up.

  • How does the video suggest solving for the time the ball is in the air?

    -The video suggests solving for the time the ball is in the air by looking at the Y direction, using the equation for displacement under constant acceleration.

  • What is the acceleration due to gravity used in the equations in the video?

    -The acceleration due to gravity used in the equations is 9.8 m/s².

  • What is the time calculated for the ball to fall from the height of the building?

    -The time calculated for the ball to fall from the height of the building is 2 seconds.

  • How is the minimum velocity (V not) calculated in the video?

    -The minimum velocity (V not) is calculated by dividing the distance D (100 meters) by the total time the ball is in the air (4 seconds), resulting in 25 m/s.

  • What additional resources does the video offer for further help with physics problems?

    -The video offers free homework help on Twitch and Discord for those who need additional assistance with physics problems.

Outlines
00:00
🏙️ Bill and Ted's Physics Challenge

In this video, Alan from both low stem, coach introduces a physics problem involving Bill and Ted on separate buildings. The problem requires finding the minimum velocity needed for a super ball to be thrown from Bill to Ted, ensuring it bounces once on the ground between the buildings. The ball's trajectory and the bounce are crucial for solving the problem. Alan encourages viewers to attempt the problem before watching the solution and provides a sketch to visualize the scenario. The problem involves understanding projectile motion and the symmetry in the ball's trajectory.

Mindmap
Keywords
💡AP Physics
AP Physics is a high school course and exam offered by the College Board that covers various topics in physics. In the video, the theme revolves around solving problems related to AP Physics, specifically in the area of kinematics, which is a branch of physics that deals with the motion of objects without considering the forces that cause the motion.
💡Kinematics
Kinematics is a fundamental concept in physics that focuses on the description of motion. In the video, the problem-solving process involves applying kinematic equations to determine the minimum velocity required for a ball to travel between two buildings, illustrating the practical application of kinematics in solving real-world problems.
💡Projectile Motion
Projectile motion is a type of motion experienced by an object or particle that is thrown near the Earth's surface and moves along a curved path under the action of gravity only. The video discusses how to calculate the time of flight and the velocity of a projectile, which is essential in understanding the trajectory of the ball thrown by Bill.
💡Velocity
Velocity is a vector quantity that represents the rate of change of an object's position with respect to time. In the video, finding the minimum velocity at which the ball should be thrown is crucial to ensure it reaches Ted. The script uses the term 'V not' to denote the initial velocity in the horizontal direction.
💡Distance (D)
In the context of the video, distance D refers to the separation between the two buildings. The problem requires calculating the minimum velocity needed for the ball to cover this distance between the buildings, making it a key parameter in the kinematic equations used.
💡Height (H)
Height H in the video is the vertical distance from the ground to the roof of the building from which the ball is thrown. It is used in the kinematic equations to determine the time the ball spends in the air before hitting the ground, which is crucial for calculating the total time of flight.
💡Bounce
The term 'bounce' in the video refers to the ball's behavior when it hits the ground. The script mentions that the ball bounces once before reaching Ted, which affects its trajectory and the calculations needed to determine the minimum velocity for a successful throw.
💡Symmetry
Symmetry in the video refers to the equal rise and fall of the ball's trajectory. The script suggests that the ball's path should be symmetrical, with the rise and fall being roughly equal, which helps in simplifying the calculations by assuming the time spent in the air is the same for both.
💡Acceleration
Acceleration is the rate of change of velocity of an object. In the video, the acceleration due to gravity (9.8 m/s^2) is used in the kinematic equations to calculate the time the ball spends in the air and its vertical motion, which is essential for determining the total time of flight.
💡Time of Flight
Time of flight is the total time an object spends in the air during its motion. In the video, determining the time of flight is crucial for calculating the minimum velocity needed for the ball to reach Ted. The script uses the kinematic equations to find that the ball is in the air for a total of four seconds.
Highlights

Continuing with AP physics kinematics problems.

Encouragement to try solving the problem before watching the solution.

Bill and Ted are on the roofs of two separate buildings.

The buildings are separated by a distance D.

The height of both buildings is H.

Bill throws the ball so it bounces once before reaching Ted.

The ball's initial velocity is parallel to the ground.

The goal is to find the minimum velocity V not to reach Ted.

The super ball bounces with the same horizontal velocity and negative vertical velocity.

The trajectory of the ball should be sketched for better understanding.

The ball's trajectory is symmetrical in its rise and fall.

The problem is solved by splitting the motion into x and y directions.

In the x-direction, the equation D = V naught * T is used.

In the y-direction, the equation H = 1/2 * a * T squared is used.

The time in the air is determined by the y-direction equation.

The duration of the ball's flight is calculated to be four seconds.

The minimum initial velocity V not is calculated to be 25 meters per second.

The video ends with an invitation to leave comments, like, or subscribe.

Free homework help is offered on Twitch and Discord.

Transcripts

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PhysicsKinematicsProjectile MotionAP ExamEducationalProblem SolvingSuper BallVelocityThrowingBouncing