A particle, (a mud pellet, say) of mass m strikes a smooth stationary wedge of mass M with a velocity Vo, at an angle `theta` with horizontal. If the collision is perfectly inelastic, find the :
a) velocity of the wedge just after the collision.
b) change in KE of the system (M + m) in the collision.

Explanation

(a) Let the system (M +m) move as a single mass with a velocity v.
Conserving the momentum of the system horizontally , we have `mv _(0) cos theta = (M+m) v`
This gives `v = (mv _(0) cos theta)/( M +m)`
(b) The change in KE of the system is
`Delta K = 1/2 (M +m) v ^(2) - 1/2 mv _(0) ^(2) ` where `v = (mv _(0) cos theta)/( M +m)`
This gives `Delta K = ((M+m))/( 2) (( mv _(0) cos theta ) /(M + m )) ^(2) -1/2 mv _(0) ^(2)`
`=- ( mv _(0) ^(2))/( 2) (1- (m)/( M + m ) cos ^(2) theta ) = - ((M + m sin ^(2) theta) mv _(0) ^(2))/( 2 (M + m ))`