A rubber ball of mass `0 *4` kg hits the ground at same angle without any change in speed . If the speed of ball is 1 m/s and the period of contact between the ball and floor is `0*4` s, find the average force exerted by the ball on the ground .

Explanation

The situation is shown in figure
The intial momentum is ` m vec(u) = m(u cos theta hat(j) - u sin theta hat (j))`
The final momentum, is `m vec(v) = m (u cos theta hat (i) + u sin theta hat (j))`
Change in momentum of the ball = ` (m(vec(v)-vec(u)))/(Deltat) = 2 "mu" sin theta hat (j)`
` rArr " The average force on the ball by the ground is " vec (F) _(av) = (Delta vec(P))/(Deltat) = (2mu sin theta hat(j))/(Delta t)`
` :. "Force exerted by the ball on the ground is " (-2"mu" sin theta)/(Deltat)("an equal and opposite force by Newton's third law")`
Therefore , ` F = (2 xx 0*4 xx sin 30^(@))/(0*4)` = 1N , along the normal .