A 0.697-kg basketball is dropped out of a window that is 6.98 m above the ground. The ball is caught by a person whose hands are 1.73 m above the ground. (a) How much work is done on the ball by its weight? What is the gravitational potential energy of the basketball, relative to the ground, when it is (b) released and (c) caught? (d) What is the change (PEf - PE0) in the ball's gravitational potential energy?

To answer this question, we need to calculate the work done by the weight of the basketball, as well as the gravitational potential energy at different points.

(a) Work done by weight:
Work is calculated using the formula:
Work = Force × Distance × cos(angle)

In this case, the force can be calculated as the weight of the basketball, which is equal to its mass multiplied by the acceleration due to gravity.
Weight = mass × acceleration due to gravity

Using the given values, we can calculate:
Weight = 0.697 kg × 9.8 m/s^2 = 6.837 N

The distance is the vertical distance the basketball falls, which is 6.98 m.

Since the angle between the force (weight) and the distance is 0 degrees (cos(0) = 1), the equation becomes:
Work = 6.837 N × 6.98 m = 47.7136 J

Therefore, the work done by the weight of the basketball is 47.7136 Joules.

(b) Gravitational potential energy when released:
The gravitational potential energy at a given height is given by the equation:
Potential Energy = mass × gravity × height

Using the given values:
Potential Energy = 0.697 kg × 9.8 m/s^2 × 6.98 m = 46.1996 J

Thus, when the basketball is released, its gravitational potential energy is 46.1996 Joules relative to the ground.

(c) Gravitational potential energy when caught:
The height at which the ball is caught is 1.73 m. Therefore:
Potential Energy = 0.697 kg × 9.8 m/s^2 × 1.73 m = 11.5732 J

Thus, when the basketball is caught, its gravitational potential energy is 11.5732 Joules relative to the ground.

(d) Change in gravitational potential energy:
The change in gravitational potential energy can be calculated as the difference between the potential energy when caught and when released:
Change in Potential Energy = Potential Energy when caught - Potential Energy when released

Using the values we calculated:
Change in Potential Energy = 11.5732 J - 46.1996 J = -34.6264 J

Therefore, the change in the ball's gravitational potential energy is -34.6264 Joules.