Question

A 150 kg bumper car moves forward at +10.0 m/s. It collides with a stationary, 200 kg bumper car. After the collision, the 200 kg bumper car moves forward at 8.57 m/s. What is the 150 kg bumper car’s velocity after the collision? Report your answer to 3 significant figures.

Answer 1

The velocity of the 150 kg bumper car after the collision is -1.427 m/s.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are involved.

Let's denote the velocity of the 150 kg bumper car after the collision as v. We have:

Mass of bumper car A (150 kg) * Initial velocity of bumper car A (+10.0 m/s) + Mass of bumper car B (200 kg) * Initial velocity of bumper car B (0 m/s) = Mass of bumper car A (150 kg) * Final velocity of bumper car A (v) + Mass of bumper car B (200 kg) * Final velocity of bumper car B (8.57 m/s)

Using the given values, we can solve for v:

(150 kg * 10.0 m/s) + (200 kg * 0 m/s) = (150 kg * v) + (200 kg * 8.57 m/s)

Simplifying the equation, we get:

1500 kg * m/s = 150 kg * v + 1714 kg * m/s

Subtracting 150 kg * v from both sides:

1500 kg * m/s - 150 kg * v = 1714 kg * m/s

Subtracting 1500 kg * m/s from both sides:

-150 kg * v = 214 kg * m/s

Dividing both sides by -150 kg:

v = -1.427 m/s

Therefore, the velocity of the 150 kg bumper car after the collision is -1.427 m/s.