# Collision

#### Mokhtar

I m having trouble solving this problem, any help plz?

#### topsquark

Forum Staff
In the first part:
Momentum will be conserved so $$\displaystyle P_f = P_i$$. We know that there is a kinetic energy loss, so $$\displaystyle KE_f = f \cdot KE_i$$.

Choose a positive direction to the right. I'm going to say that car 1 is moving to the right initially. I'm going to call the initial velocities of the cars $$\displaystyle v_1$$ and $$\displaystyle v_2$$. Here's the setup:
Momentum:
$$\displaystyle m_1 v_{1f} + m_2 v_{2f} = m_1 v_1 - m_2 v_{2f}$$

and Energy:
$$\displaystyle \dfrac{1}{2} m_1 v_{1f}^2 + \dfrac{1}{2} m_2 v_{2f}^2 = f \cdot \left ( \dfrac{1}{2} m_1 v_1^2 + \dfrac{1}{2} m_2 v_2^2 \right )$$

You know that $$\displaystyle m_1 = m_2 = m$$ and $$\displaystyle v_2 = v_1 = v$$.

See what you can do with this and let us know what you've been able to do.

-Dan