Question

A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is ______. (Take g = 9.8 m/s²)

विकल्प

• 21 Ns

• 7 Ns

• 0

• 84 Ns

Answer 1

A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is 21 Ns.

Explanation:

Let u = velocity of ball striking the ground

= `sqrt(2gh)`

= `sqrt(2 xx 9.8 xx 40)`

= 28 m/s

Let v = rebound velocity

= `sqrt(2gh')`

= `sqrt(2 xx 9.8 xx 10)`

= 14 m/s

Impulse `vecJ` = change in momentum

= `vecP_f - vecP_i`

= `m(vecv - vecu)`

= `0.5[14hatj - 28(-hatj)]`

= `0.5(14hatj + 28hatj)`

= `0.5(42hatj)`

= `21hatj`

`|vecJ| = 21 Ns`