A ball of mass 0.15kg is dropped from a height 10m strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (`g = 10 m/s^2`) nearly:

Options

A. `4.2 kgm//s`
B. `2.1 kgm//s`
C. `1.4 kgm//s`
D. `0 kgm//s`

Answer

A

Explanation

Velocity just before striking the ground
`v_1 = sqrt(2gh)`
`v_1=sqrt(2(10)(10))=10sqrt2m//s`
`v_1=-10 sqrt2hatj`
If it reaches the same height, speed remains same after collision only the direction changes
`v_2 =10sqrt2 m//s`
`vecv_2 = 10 sqrt2 hatj`
|Impulse| = m `|(Deltavecv|)`
`=m |10sqrt2j-(-10sqrt2j)|`
`= 0.15[2(10sqrt2)]`
`=3sqrt2 kgm//s = 4.2 kgm//s`