A 71.5 kg ice skater moving to the right with a velocity of 2.92 m/s throws a 0.16 kg snowball to the right with a velocity of 20.1 m/s relative to the ground.
To find the final velocity of the ice skater after throwing the snowball, you need to use the principle of conservation of momentum. The total momentum before the snowball is thrown is equal to the total momentum after the snowball is thrown.
The momentum of an object is given by the equation:
momentum = mass * velocity
Let's start by finding the initial momentum of the ice skater and the snowball:
Initial momentum of ice skater = mass of ice skater * velocity of ice skater
= 71.5 kg * 2.92 m/s
Initial momentum of snowball = mass of snowball * velocity of snowball
= 0.16 kg * 20.1 m/s
The total initial momentum is the sum of the initial momentum of the ice skater and the snowball:
Total initial momentum = Initial momentum of ice skater + Initial momentum of snowball
Now, let's find the final momentum of the ice skater after throwing the snowball. Since the snowball is thrown to the right, the ice skater will experience an equal and opposite momentum to the left.
Final momentum of ice skater = Total initial momentum - Initial momentum of snowball
To find the final velocity of the ice skater, we need to use the equation:
momentum = mass * velocity
Rearranging the equation to solve for velocity gives:
velocity = momentum / mass
Final velocity of ice skater = Final momentum of ice skater / mass of ice skater
Now, let's calculate the final velocity:
Final velocity of ice skater = (Total initial momentum - Initial momentum of snowball) / mass of ice skater
Plug in the given values:
Final velocity of ice skater = (71.5 kg * 2.92 m/s - 0.16 kg * 20.1 m/s) / 71.5 kg
Now solve for the final velocity of the ice skater.