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

We apply the momentum preservation principle and we have.
p(before)=p(after)
0=1000×250-25m
m=10000kg or 10 tonns

Answer 2

The mass of the asteroid is 10,000 kg.

Step-by-step explanation:

It is given that,

Mass of the spacecraft, m₁ = 1000 kg

Velocity of spacecraft, v₁ = 250 m/s

Velocity of asteroid, v₂ = -25 m/s

We have to find the mass of the asteroid. It is also assumed that there is no net force on the system. So, the momentum remains conserved. According to law of conservation of momentum :

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

Where

u₁ and u₂ are initial velocity of spacecraft and asteroid

and v₁ and v₂ are final velocity of spacecraft and asteroid

`0=1000\ kg* 250\ m/s+m_2* (-25\ m/s)`

On solving : m₂ = 10,000 kg

Hence, the mass of the asteroid is 10,000 kg.