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

Option C 10,000 kg

Step-by-step explanation:

Answer 2

Answer: 10000 kg

Step-by-step 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