What Happens When a Person Throws a Helmet on Ice Skates?

Calculation of Final Speed:

A person with a mass of 50 kg is standing still on ice skates. They throw their 2.0 kg helmet to the right at a speed of 25 m/s on a frictionless surface. By applying the principle of conservation of momentum, we can calculate the final speed of the person.

According to the conservation of momentum, the initial momentum of the system (person + helmet) must be equal to the final momentum of the system. The momentum of an object is calculated as the product of its mass and velocity.

The initial momentum of the system is the momentum of the person before throwing the helmet, which is 0 because the person is standing still. The momentum of the helmet can be calculated as:

Momentum of the helmet (initial) = mass x velocity = 2.0 kg x 25 m/s = 50 kg m/s

Since momentum is conserved, the final momentum of the system (person + helmet) must also be 50 kg m/s. Since the person was initially at rest, the final momentum is only due to the person's motion after throwing the helmet.

Let v be the final velocity of the person after throwing the helmet. The final momentum of the person is:

Momentum of the person (final) = mass x velocity = 50 kg x v

Setting the initial and final momentum equal gives:

50 kg = 50 kg x v

Solving for v:

v = 50 kg / 50 kg = 1.0 m/s

Therefore, the final speed of the person after throwing their helmet on the ice skates is 1.0 m/s to the right.