Question

A car with a mass of 1.1 × 103 kilograms hits a stationary truck with a mass of 2.3 × 103 kilograms from the rear end. The initial velocity of the car is +22.0 meters/second. After the collision the velocity of the car is -11.0 meters/second. What is the velocity of the truck after this elastic collision?

+13 meters/second
+20 meters/second
+15.7 meters/second
+7.5 meters/second
+9.8 meters/second

Answer 1

By the principle of conservation of linear momentum: in an elastic collision, the sum of both initial momenta (mass * velocity) equals the sum of both final momenta. \[m _{a}v_{1a} + m _{b}v_{1b} = m _{a}v_{2a} + m _{b}v_{2b}\]

If you choose the car to be object 'a', (it doesn't matter which one you choose to be object 'a', as long as you are consistent throughout the problem), then you know that:

\[m _{a} = 1.1 x 10^{3} kg\]
\[m _{b} = 2.3 x 10^{3} kg\]
\[v _{1a} = +22 m/s\]
\[v _{1b} = 0 m/s\]
\[v _{2a} = -11 m/s\]
\[v _{2b} = ? m/s\]