Question

The parking brake on a $2000\mathrm{kg}$Cadillac has failed, and it is rolling slowly, at $1.0\mathrm{mph}$, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your $1000\mathrm{kg}$ Volkswagen head-on into the Cadillac and save the children. With what speed should you impact the Cadillac to bring it to a halt?

Short answer

The speed will be$2\mathrm{mph}.$

Step-by-step solution

Given information

We have given,

speed of Cadillac =$1\mathrm{mph}$

Mass of Cadillac=$2000\mathrm{kg}$

Mass of Volkswagen =$1000\mathrm{kg}$

We have to find the speed of Volkswagen.

Simplify

According to conservation of momentum, the initial momentum of the system will be same after the Collison.

$$\begin{gathered} {\mathrm{P}}_{\mathrm{I}}={\mathrm{P}}_{\mathrm{F}} \\ \mathrm{Momentum}\mathrm{of}\mathrm{Cadillac}=\mathrm{Momentum}\mathrm{of}\mathrm{Volkswagen} \\ (2000\mathrm{kg}\times 1\mathrm{mph})+(1000\mathrm{kg}\times \mathrm{V}\mathrm{mph})=(1000+2000)\times 0\mathrm{mph} \\ \mathrm{V}=2\mathrm{mph} \end{gathered}$$