Question

A 1200-kg car, C, traveling south at 25 m/s collides and locks with a 1800-kg car, D, traveling west at 30.0 m/s. At what speed do the cars move after the collision? Show your work.

Answer 1

Speed of two cars is 20.6 m/s

Step-by-step explanation:

As we know that there is no external force on the system of two cars

So momentum of the system will remain conserved before and after collision

So we will have

`P_i = m_1v_1 \hat i + m_2 v_2 \hat j`

here we know

`m_1 = 1800 kg`

`v_1 = 30 m/s` towards west

`m_2 = 1200 kg`

`v_2 = 25 m/s`

so we have

`P_i = (1800)(30)\hat i + (1200)(25)\hat j`

`P_i = 54000\hat i + 30000\hat j`

now if finally two cars locked and moved together

`P_f = (m_1 + m_2) v_f`

`54000\hat i + 30000\hat j = (1200 + 1800) \vec v`

`\vec v = 18\hat i + 10 \hat j`

so speed of two cars is given as

`v = √(18^2 + 10^2)`

`v = 20.6 m/s`