Two students in bumper cars want to prove conservation of momentum. They collide their bumper cars. The first bumper car has a mass of 120 kg and was moving with a velocity of 4 m/s before the collision and with velocity of -2 m/s after the collision. The second bumper car has a mass 90 kg and was moving at a velocity of -5 m/s before the collision. To prove conservation of momentum, what must the velocity of the second bumper car be after the collision?
A. 2.3 m/s
B. 2.7 m/s
C. 3.0 m/s
D. 1.0 m/s
To prove conservation of momentum, we need to analyze the momentum before and after the collision.
The momentum before the collision is given by:
Momentum1 + Momentum2 = (mass1 × velocity1) + (mass2 × velocity2)
= (120 kg × 4 m/s) + (90 kg × -5 m/s)
= 480 kg·m/s - 450 kg·m/s
= 30 kg·m/s
After the collision, we can use the conservation of momentum equation:
Momentum1 + Momentum2 = (mass1 × velocity1) + (mass2 × velocity2)
= (120 kg × -2 m/s) + (90 kg × velocity2)
= -240 kg·m/s + 90 kg × velocity2
Since we know the initial momentum was 30 kg·m/s, we can equate the two equations and solve for velocity2:
30 kg·m/s = -240 kg·m/s + 90 kg × velocity2
270 kg·m/s = 90 kg × velocity2
velocity2 = 270 kg·m/s / 90 kg
velocity2 = 3 m/s
Therefore, the velocity of the second bumper car after the collision must be 3 m/s.
The correct answer is C. 3.0 m/s.