Answer:
The approximate velocity the rocket must have to stop the asteroid completely after the collision is;
C. -324 m/s
Step-by-step 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.