Question

A $1500\mathrm{kg}$car is rolling at $2.0\mathrm{m}/\mathrm{s}$. You would like to stop the car by firing a $10\mathrm{kg}$blob of sticky clay at it. How fast should you fire the clay?

Short answer

The speed of the clay should be$300\mathrm{m}/\mathrm{s}.$

Step-by-step solution

Step 1; Given information

We have given,

$$\begin{gathered} \mathrm{Mass}\mathrm{of}\mathrm{car}=1500\mathrm{kg} \\ \mathrm{Mass}\mathrm{of}\mathrm{clay}=10\mathrm{kg} \\ \mathrm{speed}\mathrm{of}\mathrm{car}=2\mathrm{m}/\mathrm{s} \end{gathered}$$

We have to find the speed of clay to stop the car.

Simplify

According to conservation of momentum .

${\mathrm{P}}_{\mathrm{I}}={\mathrm{P}}_{\mathrm{F}}$

since the velocity of the car and clay is zero in the final then its momentum will be also zero.

Then we can write,

$$\begin{gathered} \left|\mathrm{Momentum}\mathrm{of}\mathrm{car}\right|=\left|Momentumofclay\right| \\ \left|M_{CAR}\times V_{CAR}\right|=\left|M_{CLAY}\times V_{CLAY}\right| \\ 1500kg\times 2m/s=10kg\times V \\ V=300m/s \end{gathered}$$