A Tennis Ball Bounces On The Floor Three Times?
A tennis ball bounces on the floor three times. The first bounce is one-half the height of the second bounce. The third bounce is one-fourth the height of the second bounce. What is the total height of the three bounces?
A tennis ball bounces on the floor three times. The first bounce is one-half the height of the second bounce. The third bounce is one-fourth the height of the second bounce. What is the total height of the three bounces?
Introduction
A tennis ball is dropped onto a hard floor from a height of 1.5 meters. It bounces three times before coming to rest. How high does the ball bounce on the third bounce?
To answer this question, we need to understand how a tennis ball behaves when it hits the ground. When a tennis ball hits the ground, it compresses slightly, and then springs back to its original shape. The force of the impact is equal to the force with which the ball rebounds.
The formula for the height of the third bounce can be derived from Newton’s laws of motion. The formula is:
h = -1/8 * g * t^2 + v0 * t – 1/2 * h0
where h is the height of the third bounce, g is the acceleration due to gravity (9.8 m/s^2), t is the time since the beginning of the third bounce, v0 is the velocity of the ball at the beginning of the third bounce, and h0 is the height of the ball at the beginning of the third bounce.
Three Bounces
When a tennis ball bounces on the floor, it hits the floor with a force that is equal to its weight. This force causes the ball to compress slightly and then rebound. The ball rebounds with a force that is less than its weight because some of the energy is used to overcome the friction between the ball and the floor. The amount of energy lost depends on how much friction there is between the ball and the floor.
The average height of each bounce can be calculated using the following equation:
h = (1/2) * g * t^2
where h is the height of each bounce, g is the acceleration due to gravity (9.81 m/s^2), and t is the time that the ball spends in contact with the floor during each bounce.
If we assume that each bounce lasts for 0.1 seconds, then we can calculate that the average height of each bounce will be:
h = (1/2) * 9.81 * 0.1^2 = 0.49 m
Conclusion
After bouncing three times, a tennis ball will eventually come to a stop. The specific amount of bounces will depend on the size and weight of the ball, as well as the surface it is bouncing on. If you are interested in how many times a tennis ball will bounce, you can experiment with different balls and surfaces to find out.
