1. A 0.20 kg ball is thrown straight up from the edge of a 30.0 m tall building at a velocity of22.0 m/s. The ball moves up to the maximum height and then falls to the ground at the baseof the building. Use the law of conservation of energy to answer the following questions,assuming that the reference level for gravitational potential energy is ground level. T/I(a) What is the total energy of the ball at the start when it had a velocity of 22.0 m/s? [ans: 110 J](b) What is the velocity of the ball at the maximum height? What is the maximum height of the ball?

(a) The total energy of the ball at the start can be calculated using the formula for kinetic energy (KE = 1/2mv^2) and potential energy (PE = mgh).

The kinetic energy (KE) of the ball at the start is given by the formula KE = 1/2mv^2, where m is the mass of the ball (0.20 kg) and v is the velocity (22.0 m/s).

KE = 1/2 * 0.20 kg * (22.0 m/s)^2 = 48.4 J

The potential energy (PE) of the ball at the start is given by the formula PE = mgh, where m is the mass of the ball (0.20 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the building (30.0 m).

PE = 0.20 kg * 9.8 m/s^2 * 30.0 m = 58.8 J

The total energy of the ball at the start is the sum of the kinetic energy and the potential energy.

Total Energy = KE + PE = 48.4 J + 58.8 J = 107.2 J

(b) At the maximum height, the velocity of the ball is 0 m/s because it has reached its peak and is about to change direction to fall back down.

The maximum height of the ball can be calculated by setting the kinetic energy at the maximum height (which is zero, because the ball is not moving) equal to the potential energy at the maximum height (which is mgh, where h is the maximum height).

0 = mgh - KE_start

Solving for h gives:

h = KE_start / (mg) = 48.4 J / (0.20 kg * 9.8 m/s^2) = 24.7 m

However, this is the height above the starting point, so the total height above the ground is the height of the building plus this value:

Total height = h_building + h = 30.0 m + 24.7 m = 54.7 m

So, the maximum height of the ball above the ground is 54.7 m.