Bumper cars have elastic collisions with each other, but inelastic collisions with people! For problems #16 - #18 assume you are riding a bumper car on a frictionless surface...

Your bumper car is travelling at 2m/s . The total mass of you and your car is 350kg. An empty motionless bumper car with a mass of 250kg is in your path. How fast in m/s will the empty bumper car move after you collide with it head on?

1 answer

To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.

Let's denote the velocity of the empty bumper car after the collision as v_final and the mass of the empty bumper car as m_empty. The velocity of your bumper car before the collision is 2 m/s, and the total mass of you and your car is 350 kg.

Using the law of conservation of momentum, we can write the equation:

(mass of your car + mass of you) * velocity of your car = mass of empty car * velocity of empty car

(350 kg) * (2 m/s) = (250 kg) * v_final

700 kg * m/s = 250 kg * v_final

To find the velocity of the empty bumper car after the collision, we can rearrange the equation and solve for v_final:

v_final = (700 kg * m/s) / (250 kg)

v_final = 2.8 m/s

Therefore, the empty bumper car will move at a velocity of 2.8 m/s after the collision.