A ball of mass m strikes a rigid wall with speed v and gets reflected without any loss of speed, as shown in the figure.

(a) What is the magnitude of the impulse imparted to the ball by the wall?
(b) What is the direction of the force on the wall due to the ball?

Explanation

Considering x-axis and y-axis as shown,
(a) `vecp_(i)=mv sin30^(@)hati-mv cos30^(@) hatj`
`vecp_(f)=-mv sin30^(@)hati-mv cos 30^(@)hatj`
`therefore Delta vecp=vecp_(f)-vecp_(i)`
`=-2 mv sin 30^(@)hati= -mv hati`
`|vec(Deltap)|=mv`.
(b) Negative sign of the impulse shows that it is along negative x-direction. Since impulse and force are in the same direction, the force on the ball is along the negative direction of x-axis. Hence the force on the wall will be along positive x-axis.