A 66.5 kg ice skater moving to the right with a velocity of 2.09 m/s throws a 0.14 kg snowball to the right with a velocity of 22.5 m/s relative to the ground.
(a) What is the velocity of the ice skater after throwing the snowball? Disregard the friction between the skates and the ice.
m/s to the right
(b) A second skater initially at rest with a mass of 61.00 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision?
m/s to the right
for (a) just conserve momentum:
(66.5+0.14)*2.09 = 66.5v + 0.14*22.5
v = 2.047
do (b) the same way. just consider the snowball and the skater before and after the collision.
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the event (throwing the snowball) is equal to the total momentum after the event.
(a) To find the velocity of the ice skater after throwing the snowball, we first need to calculate the initial momentum of the ice skater.
Initial momentum of the ice skater = mass of the ice skater × velocity of the ice skater
Substituting the given values:
Initial momentum = 66.5 kg × 2.09 m/s
Now, let's calculate the momentum of the snowball before the event. The momentum of an object is given by its mass multiplied by its velocity.
Momentum of the snowball before throwing = mass of the snowball × velocity of the snowball
= 0.14 kg × 22.5 m/s
Since the snowball is thrown in the same direction as the ice skater's initial velocity, we can add the two momentum values together to get the total momentum after the event.
Total momentum after the event = Initial momentum of the ice skater + Momentum of the snowball before throwing
Now, divide the total momentum after the event by the total mass of the system (ice skater + snowball) to find the velocity of the ice skater after throwing the snowball.
Velocity of the ice skater after throwing the snowball = Total momentum after the event / (mass of the ice skater + mass of the snowball)
(b) For the second part of the question, we need to consider a perfectly inelastic collision. In this type of collision, the two objects stick together after the collision, and their velocities become the same.
To find the velocity of the second skater after catching the snowball, we again use the principle of conservation of momentum. The total momentum before the event is equal to the total momentum after the event.
The initial momentum of the second skater is zero since they are initially at rest.
Total initial momentum = Initial momentum of the snowball + Initial momentum of the ice skater
Now, divide the total momentum before the event by the total mass of the second skater and the snowball together to find the velocity of the second skater after catching the snowball in a perfectly inelastic collision.
Velocity of the second skater after catching the snowball = Total momentum before the event / (mass of the second skater + mass of the snowball)
Note: In both calculations, make sure to include the sign (positive or negative) indicating the direction of the velocity.