Question

a 0.199 kg snowball moving west makes an inelastic collision with a 2.89 kg box moving 0.523 m/s west. afterward,they move west at 1.92 m/s. what was the initial velocity of the snowball? PLEASE HELP MEEEEE

Answer 1

The initial velocity of the snowball was 22.21 m/s

Step-by-step explanation:

Since the collision is inelastic, only momentum is conserved. And since the snowball and the box move together after the collision, they have the same final velocity.

Let
`m_1` be the mass of the ball, and
`v_1` be its initial velocity; let
`m_2` be the mass of the box, and
`v_2` be its velocity; let
`v_f` be the final velocity after the collision, then according to the law of conservation of momentum:

`m_1v_1+m_2v_2=v_f(m_1+m_2)`.

From this we solve for
`v_1`, the initial velocity of the snowball:

`\boxed{v_1=(v_f(m_1+m_2)-m_2v_2)/(m_1)}`

now we plug in the numerical values
`m_1=0.199\:kg`,
`m_2=2.89\:kg`,
`v_2=0.523\:m/s`, and
`v_f=1.92\:m/s` to get:

`v_1=(1.92*(0.199+2.89)-2.89*0.523)/(0.199)`

`\boxed{v_1=22.21\:m/s}`

The initial velocity of the snowball is 22.21 m/s.

P.S: we did not take vectors into account because everything is moving in one direction—towards the west.