Question

A small 1.0 kg steel ball rolls west at 3.0 m/s collides with a large 3.0 kg ball at rest. After the collision, the small ball moves south at 2.0 m/s. What is the direction of the momentum (with respect to east) of the large ball after the collision

Answer 1

The direction of the momentum of the large ball after the collision with respect to east is 146.58°.

Step-by-step explanation:

Given that,

Mass of large ball = 3.0 kg

Mass of steel ball = 1.0 kg

Velocity = 3.0 kg

After collision,

Velocity = 2.0 m/s

Using conservation of momentum

`m_(1)u_(1)+m_(2)u_(2)=m_(1)v_(1)+m_(2)v_(2)`

`3.0*0+1.0*(3.0)(-i)=1.0*2(-j)+3.0* v_(2)`

`-3i+2j=3.0* v_(2)`

`v_(2)=-i+0.66j`

The direction of the momentum

`tan\theta=(0.66)/(-1)`

`\theta=tan^(-1)(0.66)/(-1)`

`\theta=-33.42^(\circ)`

The direction of the momentum with respect to east

`\theta=180-33.42=146.58^(\circ)`

Hence, The direction of the momentum of the large ball after the collision with respect to east is 146.58°.