Question

A 50 kg person standing still in ice skates throws their 2 kg helmet to the right at 25 m/s while on a frictionless surface.

What is the final speed of the person?

Answer 1

Step-by-step explanation:

Let's denote:

m1 = mass of the person = 50 kg

m2 = mass of the helmet = 2 kg

v2 = velocity of the helmet = 25 m/s (magnitude)

The total initial momentum is zero, and the total final momentum is also zero (due to conservation of momentum).

Initial Momentum = 0 = m1 * v1 + m2 * v2

Final Momentum = 0 = m1 * v1' + m2 * v2'

Since the person starts moving in the opposite direction, the final velocity of the person (v1') will be in the opposite direction to the initial velocity of the helmet (v2).

we can solve for v1' (final velocity of the person):

0 = m1 * v1' + m2 * (-v2)

0 = 50 kg * v1' - 2 kg * 25 m/s

50 kg * v1' = 2 kg * 25 m/s

v1' = (2 kg * 25 m/s) / 50 kg

v1' = 50 m/s

So, the final speed of the person is 50 m/s in the opposite direction to the thrown helmet