a .5kg ball is dropped from a 30m high building is on the ground for 2ms then bounces up 20m. What avg force was exerted on the ball?

To calculate the average force exerted on the ball, we can use the concept of work and energy. The average force can be determined by considering the change in the ball's kinetic energy during its motion.

First, let's analyze the ball when it is dropped from the 30m high building. At this point, the ball has a gravitational potential energy due to its height. We can calculate this potential energy using the equation:

Potential Energy = mass * acceleration due to gravity * height

Given:
mass (m): 0.5 kg
height (h): 30 m
acceleration due to gravity (g): 9.8 m/s^2

Potential Energy = 0.5 kg * 9.8 m/s^2 * 30 m = 147 J

When the ball hits the ground, all of its potential energy is converted into kinetic energy. Thus, the initial kinetic energy of the ball upon hitting the ground is equal to the potential energy:

Initial Kinetic Energy = 147 J

The ball then bounces up a height of 20m. At this point, the ball again has potential energy. Using the same equation as before, we can calculate this potential energy:

Potential Energy = mass * acceleration due to gravity * height

Given:
mass (m): 0.5 kg
height (h): 20 m
acceleration due to gravity (g): 9.8 m/s^2

Potential Energy = 0.5 kg * 9.8 m/s^2 * 20 m = 98 J

At the highest point of its bounce, the ball has momentarily stopped and therefore its kinetic energy is zero.

The change in kinetic energy can be calculated as the difference between the initial and final kinetic energies:

Change in Kinetic Energy = Initial Kinetic Energy - Final Kinetic Energy
Change in Kinetic Energy = 147 J - 0 J = 147 J

Now, we can calculate the average force exerted on the ball. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied. In this case, the work done on the ball is equal to the change in kinetic energy.

Work Done = Force * Distance

Since the average force is exerted over the entire distance the ball traveled (30 m + 20 m = 50 m), the equation becomes:

Average Force = Work Done / Distance
Average Force = Change in Kinetic Energy / Distance
Average Force = 147 J / 50 m
Average Force = 2.94 N

Therefore, the average force exerted on the ball is approximately 2.94 Newtons.