Physics

To calculate the impulse and the work done on the football, we use the following formulas:

Impulse:

Impulse is the change in momentum, given by:

Where:

(mass of the football)

(initial velocity of the football, toward the goalkeeper)

(final velocity of the football, after being struck by the goalkeeper; negative because it changes direction)

The change in velocity is:

Now, calculate the impulse:

The magnitude of the impulse is:

Work Done:

Work is related to the change in kinetic energy: