Question

At the local destruction derby a 400 kg Toyota moving at 10 m/s collides with an 800 kg Chevy. Both are at rest after the collision. What was the velocity of the Chevy before the collision?​

Answer 1

`u_2 = -5m/s`

Step-by-step explanation:

Given

Before Collision

Toyota

`mass = m_1 = 400kg`

`iniital\ velocity = u_1 =10m/s`

Chevy

`mass = m_2=800kg`

`initial\ velocity = u_2 = ??`

After Collision

Both Toyota and Chevy

`final\ velocity = v = 0m/s`

Required

Determine the initial velocity of Chevy

This question will be answered using the following law of conservation of momentum which states that:

`m_1u_1 + m_2u_2 = (m_1 + m_2)v`

Substitute values for m1, m2, u1 and v

`400 * 10 + 800 * u_2 = (400 + 800) * 0`

`4000 + 800u_2 = (1200) * 0`

`4000 + 800u_2 = 0`

Collect Like Terms

`800u_2 = 0 - 4000`

`800u_2 = -4000`

Divide through by 800

`(800u_2 = -4000)/(800)`

`u_2 = (-4000)/(800)`

`u_2 = -5m/s`

The velocity of Chevy before collision was 5m/s in the opposite direction of Toyota