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. a) 100 kg b) 6,250 kg c) 10,000 kg d) 6,250,000 kg

The mass of the asteroid is 10,000 kg.

Momentum is the product of mass and velocity. From the principle of conservation of linear momentum, the momentum before collision is equal to the momentum after collision.

Hence;

1000 Kg × 250 m/s = -25 m

m = 1000 × 250/25

m = 10,000 kg

The mass of the asteroid is 10,000 kg.

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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