Final answer:
The work required to stop the ball is -32 joules, which is the amount of work needed to counteract the ball's initial kinetic energy of +32 joules.
Step-by-step explanation:
To calculate the work done to stop the ball, we need to apply the concept of kinetic energy. The kinetic energy (KE) of a moving object can be calculated using the formula KE = ½ mv², where m is the mass of the object and v is its velocity. To stop the ball, the work done must be equal to its initial kinetic energy but with the opposite sign. Considering that the mass (m) of the ball is 160 g (0.16 kg) and its initial velocity (v) is 20 m/s, its kinetic energy can be calculated as follows:
KE = ½ (0.16 kg)(20 m/s)² = 32 J
Therefore, the work required to stop the ball is -32 J (negative to indicate that the work is done against the motion of the ball).