A riding ball of mass `m` strikes a rigid wall at `60^(@)` and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be.

Options

A. Mv
B. 2mV
C. `(mV)/(2)`
D. `(mV)/(3)`

Answer

A

Explanation

Given, `p_(i)=p_(f)=Mv`
Change in momentum of the ball=`bar(p)_(f)=bar(p)_(i)`
`=(-p_(f_(x))hati-p_(f_(y))hatj)-(p_(i_(x))hati-p_(i_(y))hatj)`
`=-hati(p_(f_(x))-p_(ix))-hatj(p_(f_(y))-p_(i_(y)))`
`=-2hatip_(ixhati)=-mVhati[therefore p_(f_(y))-p_(iy)=0]`
`"Here"p_(ix)-p_(fx)cos 60^(@)=(mV)/(2)`
Impulse imparted by the wall=Change in the momentum of the ball=mV