Question

A 27.0 g marble sliding to the right at 56.8 cm/s overtakes and collides elastically with a 13.5 g marble moving in the same direction at 14.2 cm/s. After the collision, the 13.5 g marble moves to the right at 71 cm/s. Find the velocity of the 27.0 g marble after the collision.

Answer 1

Answer:
`v_1=28.4 cm/s`

Step-by-step explanation:

Given

mass of marble
`m_1=27 gm`

velocity of marble
`u_1=56.8 cm/s \approx 0.568 m/s`

mass of second marble
`m_2=13.5 gm`

Velocity of second marble
`u_2=14.2 cm/s \approx 0.142 m/s`

After collision 13.5 gm marble moves to the right at i.e.
`v_2=71 cm/s`

Conserving momentum

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

`27* 56.8+13.5* 14.2=27* v_1+13.5* 71`

`1533.6+191.7=27\cdot v_1+958.5`

`27\cdot v_1=766.8`

`v_1=(766.8)/(27)=28.4 cm/s`