Question

A NASA explorer spacecraft with a mass of 1,000 kg takes off in a positive direction from a stationary asteroid. If the velocity of the spacecraft is 250 m/s and the asteroid is pushed back –25 m/s, what is the mass of the asteroid? Assume there is no net force on the system.

Answer 1

Answer: 10000 kg

Explanation:

The momentum $p$ is given by the following equation:  

$p=m.V$ (1)  

Where:  

$m$ is the mass of the object  

$V$ is the velocity of the object

Now, in this case and according the conservation of momentum:

$m_{1}v_{1}+m_{2}v_{2}=m_{1}u_{1}+m_{2}u_{2}$   (2)  

Where:

$m_{1}=1000kg$ is the mass of the spacecraft

$m_{2}$ is the mass of the asteroid

$v_{1}=0$ is the initial velocity of the spacecraft

$v_{2}=0$ is the initial velocity of the asteroid (because we are told the asteroid is stationary, as the spacracft is on the sateroid it remains stationary as well)

$u_{1}=250m/s$ is the final velocity of the spacecraft

$u_{2}=-25m/s$ is the final velocity of the asteroid

Rewritting (2):

$0=m_{1}u_{1}+m_{2}u_{2}$   (3)  

$0=(1000kg)(250m/s)+m_{2}(-25m/s)$   (4)  

Finding $m_{2}$:

$m_{2}=10000kg$ This is the mass of the asteroid

Answer 2

Answer:

Option C 10,000 kg

Explanation: