Question

Bouncing Ball The coefficient of restitution of a ball, a number between 0 and 1, specifies how much energy is conserved when the ball hits a rigid surface. A coefficient of .9, for instance, means a bouncing ball will rise to 90% of its previous height after each bounce. Write a program to input a coefficient of restitution and an initial height in meters, and report how many times a ball bounces when dropped from its initial height before it rises to a height of less than 10 centimeters. Also report the total distance traveled by the ball before this point. See Fig. 3.26. The coefficients of restitution of a tennis ball, basketball, super ball, and softball are .7, .75, .9, and .3, respectively.

Enter coefficient of restitution: .7
Enter initial height in meters: 8
Number of bounces: 13
Meters traveled: 44.82
FIGURE 3.26 Possible outcome of Exercise 16.

In Exercises 17 and 18, write a program corresponding to the flowchart.

17. Greatest Common Divisor The flowchart in Fig. 3.29 finds the greatest common divisor (GCD) of two nonzero integers input by the user. Note: The GCD of two numbers is the largest integer that divides both. See Fig. 3.27.

Enter value of M: 30
Enter value of N: 35
Greatest common divisor: 5

Answer 1

The bouncing ball's coefficient of restitution defines how much of the ball's height is recovered after each bounce. The loss of kinetic energy is attributed to air resistance, deformation, and conversion of energy into heat during the collision.

Step-by-step explanation:

In physics, when a bouncing ball hits the ground and rebounds, the coefficient of restitution (c) defines the energy conservation of the collision. A coefficient of 0.9 suggests the ball reaches 90% of the previous height after each bounce. The energy loss during each bounce is due to factors such as air resistance and deformation of the ball and surface, which convert kinetic energy into other forms of energy, mainly heat.

To explain the loss of kinetic energy, we evaluate the ball’s behavior during the collision. When the ball hits the ground, it undergoes deformation, and internal forces do work on the ball, causing heating and some permanent deformation. The energy that goes into these processes does not contribute to the ball rebounding, hence the reduced bounce height.