# 1) Two vehicles approach a right angle intersection and then collide. After the collision, they become entangled. If their mass ratios were 1:5 and their respective speeds as they approached were...

1) Two vehicles approach a right angle intersection and then collide. After the collision, they become entangled. If their mass ratios were 1:5 and their respective speeds as they approached were 16 m/s and 17 m/s, find the final velocity of the wreck.

sciencesolve | Student

You need to evaluate the final velocity, after collision, under the given conditions, such that:

`v_c = (m_1*v_1 + m_2*v_2)/(m_1 + m_2` )

`m_1, m_2` represent the masses of cars

`v_1` and `v_2` represents the velocities before collision

The problem provides the information that the masses ratio is `1/5` , such that:

`m_1/m_2 = 1/5 => m_2 = 5m_1`

The problem provides the information that the velocities of cars before collision are `v_1 = 16 m/s` and `v_2 = 17 m/s` .

Replacing `5 m_1` for m_2 and 16 for `v_1` , 17 for `v_2` , yields:

`v_c = (16m_1 + 5m_1*17)/(m_1 + 5m_1)`

Factoring out `m_1` yields:

`v_c = m_1(16 + 5*17)/(6m_1)`

Reducing duplicate factors yields:

`v_c = 85/6 => v_c = 14/16 m/s`

Hence, evaluating the final velocity, after collision, yields `v_c = 14/16 m/s.`