A NASA explorer spacecraft with a mass of 1,000 kg takes off in a positive direction from a stationary asteroid. If the velocity

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3 years ago

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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.
A) 100 kg
B) 6,250 kg
C) 10,000 kg
D) 6,250,000 kg

Physics

2 answers:

Jet001 [13] · Answer 1 · 2022-03-18T09:46:54+03:00

Before the launch, the momentum of the (spacecraft + asteroid) was zero. So after the launch, the momentum of the (spacecraft + asteroid) has to be zero.

Momentum = (mass) x (velocity)

Momentum after the launch:

Spacecraft: (1,000 kg) x (250 m/s) = 250,000 kg-m/s

Asteroid: (mass) x (-25 m/s)

Their sum: 250,000 - 25(mass) .

Their sum must be zero, so 250,000 kg-m/s = (25 m/s) x (mass)

Divide each side by 25 : 10,000 kg-m/s = (1 m/s) x (mass)

Divide each side by (1 m/s) : 10,000 kg = mass