Anasa 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. 100 kg 6,250 kg 10,000 kg 6,250,000 kg

Option C

The initial velocity of both asteroid and spacecraft is 0 m/s.

Final velocity of asteroid and spacecraft is -25 m/s and 250 m/s respectively.

According to law of conservation of momentum:

m_{a1}u_{a1}+m_{s2}u_{s2}=m_{a1}v_{a1}+m_{s2}v_{s2}

here, a stands for asteroid and s for space craft.

u is initial velocity and v is final velocity thus,

0=m_{a1}×(-25 m/s)+(1000 kg)(250 m/s)

Rearranging,

m_{a1}=\frac{(1000 kg)(250 m/s)}{(25 m/s)}=10000 kg

Thus, option C is correct.

C

Explanation: