A ball of mass `m` moving with velocity `v_(0)` collides with a wall as shown in Fig. After impact it rebounds with a velocity' `(v_(0))//2`The component of impulse acting on the ball along the wall is

Options

A. `(mv_(0))/2hatj`
B. `-(mv_(0))/2hatj`
C. `-(mv_(0))/5hatj`
D. none of these

Answer

C

Explanation

Component of initial momentum along the wall is
`P_(iy)=mv_(0)sin37^(@)hatj`
component of final momentum along the wall is
`P_(iy)=(mv_(0)) sin37^(@)hatj`
`P_(fy)=(mv_(0))/2sin53^(@)hatj`
So, component of impulse along the wall is `J_(y)=P_(fy)-P_(iy)`
`(mv_(0))/2xx4/5-(mv_(0))/1xx3/5hatj=-(mv_(0))/5hatj`