Question

scientists observe an approaching asteroid that is on a collision course with earth. they devise a plan to launch a rocket that will collide with inelastically and stop it. the mass of the asteroid is 9000 kg, and it is approaching earth at 45 m/s. if the rocket has a mass of 1800 kg, what velocity must it have to completely stop the asteroid after collision?

a. 306 m/s
b. - 225 m/s
c. - 116 m/s
d. 45 m/s

Explanation:

Step1: Apply conservation of momentum

The initial momentum of the system is the sum of the momentum of the asteroid and the rocket. After in - elastic collision, they stop, so the final momentum is 0. Let the velocity of the rocket be $v$. The momentum of the asteroid $p_{a}=m_{a}v_{a}$ and the momentum of the rocket $p_{r}=m_{r}v$. According to the law of conservation of momentum $p_{i}=p_{f}$, so $m_{a}v_{a}+m_{r}v = 0$.

Step2: Solve for the velocity of the rocket

We know $m_{a}=9000$ kg, $v_{a}=45$ m/s, and $m_{r}=1800$ kg. Rearranging the equation $m_{a}v_{a}+m_{r}v = 0$ for $v$ gives $v=-\frac{m_{a}v_{a}}{m_{r}}$. Substitute the values: $v =-\frac{9000\times45}{1800}$.
$v=- 225$ m/s.

Answer:

B. - 225 m/s