Question

During another safety crash test, a 2550 kg truck traveling east at 19.5 m/s crashes into a 1780 kg compact car that is traveling west at 39.2 m/s. The two crumple together and travel as one unit. Find their velocity and direction after impact.

Answer 1

Let's choose eastward as the positive direction. Then, we can find the velocity of the crumple after the impact from the Law of Conservation of Momentum:

$$m_1v_1-m_2v_2=(m_1+m_2)v,$$

here, $m_1=2550\ kg$ is the mass of the truck, $v_1=19.5\ \dfrac{m}{s}$ is the velocity of the truck, $m_2=1780\ kg$ is the mass of the car, $v_2=39.2\ \dfrac{m}{s}$ is the velocity of the car, $v$ is the velocity of the crumple after the impact.

Then, from this equation we can find $v$:

$$v=\dfrac{m_1v_1-m_2v_2}{m_1+m_2},$$ $$v=\dfrac{2550\ kg\cdot 19.5\ \dfrac{m}{s}-1780\ kg\cdot 39.2\ \dfrac{m}{s}}{2550+1780}=-4.63\ \dfrac{m}{s}.$$

The sign minus means that the crumple after the impact traveling west.

Answer:

$v=4.63\ \dfrac{m}{s},$ west.