Scientists observe an approaching asteroid that is on a collision course with Earth. They devise a plan to launch a rocket that will collide with the asteroid
inelastically and stop it. The mass of the asteroid is 11,000 kg, and it is
approaching Earth at 50 m/s. If the rocket has a mass of 1700 kg,
approximately what velocity must it have to completely stop the asteroid after
collision?
A. -516 m/s
B. 105 m/s
O C. -324 m/s
D. 212 m/s

The approximate velocity the rocket must have to stop the asteroid completely after the collision is;

C. -324 m/s

Explanation:

The parameters of the asteroid and the rocket are;

The mass of the asteroid, m₁ = 11,000 kg

The initial velocity with which the asteroid is approaching Earth, v₁ = 50 m/s

The mass of the rocket, m₂ = 1700 kg

The initial velocity of the rocket = v₂

The final velocity of the combined asteroid and rocket after the collision, v₃ = 0 m/s

By the law of conservation of linear momentum, we have;

The total initial momentum = The total final momentum

m₁·v₁ + m₂·v₂ = (m₁ + m₂)·v₃

Substituting the known values, we get;

11,000 kg × 50 m/s + 1,700 kg × v₂ = (11,000 kg + 1,700 kg) × 0 m/s

11,000 kg × 50 m/s + 1,700 kg × v₂ = 0

∴ 1,700 kg × v₂ = -11,000 kg × 50 m/s

v₂ = (-11,000 kg × 50 m/s)/(1,700 kg) = -323.529412 m/s ≈ -324 m/s

The approximate initial velocity the jet must have to completely stop the asteroid after the collision is -324 m/s.

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