Kinematics bouncing ball problem

In summary, the ball is bouncing elastically with a speed of 1 m/s between walls of a railway compartment of size 10 m. As seen from the ground, the direction of motion of the ball changes every time it bounces off the wall and its velocity is 1 m/s with respect to the train. The observer at the ground will see the ball moving with a velocity of 11 m/s when it moves in the same direction as the train, and with a velocity of 9 m/s when it moves backwards inside the compartment. The acceleration of the ball is the same as that of the train. Options (a), (c), and (d) are correct. Option (b) is not justified
  • #1
mridulag
2
0
given below is a more than one choice type MCQ,

A ball is bouncing elastically with a speed 1 m/s between walls of
a railway compartment of size 10 m in a direction perpendicular
to walls. The train is moving at a constant velocity of 10 m/s parallel
to the direction of motion of the ball. As seen from the ground,
(a) the direction of motion of the ball changes every 10 seconds.
(b) speed of ball changes every 10 seconds.
(c) average speed of ball over any 20 second interval is fixed.
(d) the acceleration of ball is the same as from the train.

i could not understand what observer at ground will see,is it ball velocity i.e 1m/s or ball velocity relative to train.
please give answer with an explanation
 
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  • #2
Hi mridulag, welcome to PF.

1 m/s is the speed of the ball with respect to the train.


ehild
 
  • #3
is it then 1st option be correct .Will the ball will retain its velocity 1m/s unjustyfyng option b?.
IN answer sheet b,c,d options are given correct
 
  • #4
mridulag said:
is it then 1st option be correct .Will the ball will retain its velocity 1m/s unjustyfyng option b?.
IN answer sheet b,c,d options are given correct

Inside the compartment, the direction of motion of the ball changes every time it bounces off from the compartment wall. How do you express the velocity v of an object observed from the ground, if it has some velocity v' with respect to an object, traveling with velocity V with respect to the ground ?
What is the velocity of the ball observed from the ground when it moves in the same direction as the train, and what is it when it moves backwards inside the compartment?

ehild
 
  • #5


The correct answer is (c) average speed of ball over any 20 second interval is fixed.

As an observer on the ground, you would see the ball moving at a constant speed of 1 m/s between the walls of the railway compartment. This is because the ball is bouncing elastically, meaning it will maintain its initial speed and direction after each bounce.

However, since the train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball, the ball's motion relative to the train will appear to change. This is due to the fact that the train's motion is affecting the frame of reference from which the ball's motion is being observed.

In this scenario, the ball's motion relative to the train would appear to change every 10 seconds, as the train moves 10 meters in that time and the ball bounces back and forth between the walls. However, the average speed of the ball over any 20 second interval would remain the same, as the ball is always moving at a constant speed of 1 m/s relative to the ground.

Therefore, the correct answer is (c) average speed of ball over any 20 second interval is fixed. This is because the ball's motion relative to the ground remains constant, while its motion relative to the train may appear to change.
 

1. What is the Kinematics bouncing ball problem?

The Kinematics bouncing ball problem is a physics problem that involves the motion of a ball as it bounces on a flat surface. It is used to analyze the position, velocity, and acceleration of the ball at different points in time.

2. How is the Kinematics bouncing ball problem solved?

The Kinematics bouncing ball problem can be solved by using equations of motion, such as the kinematic equations, to calculate the position, velocity, and acceleration of the ball at different points in time. Other factors such as the initial velocity, height of the ball, and gravitational acceleration can also be taken into account.

3. What are the assumptions made in the Kinematics bouncing ball problem?

The Kinematics bouncing ball problem makes certain assumptions, such as the ball being perfectly spherical, the surface being flat and rigid, and air resistance being negligible. These assumptions allow for a simplified analysis of the problem.

4. How does the Kinematics bouncing ball problem relate to real-world situations?

The Kinematics bouncing ball problem can be applied to real-world situations, such as the motion of a ball being thrown or bounced on a flat surface. It can also be used to analyze the behavior of other objects that exhibit similar motion, such as a bouncing basketball or a bouncing car on a bumpy road.

5. What are some common applications of the Kinematics bouncing ball problem?

The Kinematics bouncing ball problem has many practical applications, including sports such as basketball and tennis, where the motion of a ball is crucial. It is also used in engineering and design to understand the behavior of objects that bounce, such as car suspensions and shock absorbers. Additionally, it is used in video game programming to create realistic bouncing ball animations.

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