During a football match, the ball shot towards the goal struck the defender's foot at the speed of 10m/s and it bounced back at 20m/s. if the time of impact was 0.2 sec, and mass of the ball 1/2 kg, then the average force exerted by defender on the ball???

Let us assume that the ball bounced back in the direction exactly opposite to what it had came.

mass of ball, m= 0.5 kg

Intial momentum: p1 = 0.5 x 10 = 5 kgm/s

final momentum: p2 = 0.5 x (-20) = 10 kgm/s (negative sign due to opposite direction of motion)

Thus change in momentum, p = p2-p1 = -15 kgm/s

Rate of change of momentum, t = 0.2 s

Thus force exerted on ball = p/t = -75 N