Question

2. A 2000 kg car collides at 30 m/s into a stationary car with a mass of 2500 kg. The twocars stick together after colliding. What is the speed of the cars after the collision?

Answer 1

Take into account that the total linear momentum must conserve before and after the collision. Then, you have:

$p=p^{\prime}$

p is the momentum before the collision and p' is the momentum after the collision.

By considering the given information you have:

p = m1*v1 + m2*v2

m1 = 2000 kg

m2 = 2500 kg

v1 = 30 m/s

v2 = 0 m/s

p' = (m1 + m2)v

Replace the previous values into the equation p=p' and solve for v:

$\begin{gathered} m_1v_1+m_2v_2=(m_1+m_2)v \\ v=\frac{m_1v_1+m_2v_2}{m_1+m_2} \\ v=\frac{(2000kg)(30\frac{m}{s})+(2500kg)(0\frac{m}{s})}{2000\operatorname{kg}+2500\operatorname{kg}} \\ v=13.33\frac{m}{s} \end{gathered}$

Hence, the speed after the collision is 13.33 m/s