Ann, a 66.1 kg person throws a 0.0460 kg snowball forward with a ground speed of 31.7 m/s. Billy, with a mass of 60.5 kg, catches the snowball. Both people are on skates. Ann is initially moving forward with a speed of 2.29 m/s, and Billy is initially at rest. After the snowball is exchanged (a) What is Ann’s velocity?
b) what is Billy's velocity
Disregard friction between the skates and the ice
To find Ann's velocity, we need to calculate the momentum before and after throwing the snowball.
a) Before throwing the snowball:
The momentum of Ann before throwing the snowball can be calculated using the formula:
Momentum = Mass x Velocity
Mass of Ann = 66.1 kg
Velocity of Ann = 2.29 m/s
Momentum of Ann before throwing the snowball = 66.1 kg x 2.29 m/s
b) After throwing the snowball:
The momentum of the snowball can be calculated using the formula:
Momentum = Mass x Velocity
Mass of the snowball = 0.0460 kg
Velocity of the snowball = 31.7 m/s
Momentum of the snowball = 0.0460 kg x 31.7 m/s
Since momentum is conserved in an isolated system, the total momentum before throwing the snowball should be equal to the total momentum after throwing the snowball:
Momentum of Ann before throwing the snowball = Momentum of Ann after throwing the snowball + Momentum of the snowball
Now, we can rearrange the equation to find the velocity of Ann after throwing the snowball:
Momentum of Ann after throwing the snowball = Momentum of Ann before throwing the snowball - Momentum of the snowball
Substituting the values, we get:
Momentum of Ann after throwing the snowball = (66.1 kg x 2.29 m/s) - (0.0460 kg x 31.7 m/s)
Now, we divide the resulting momentum by Ann's mass to find her velocity:
Velocity of Ann after throwing the snowball = Momentum of Ann after throwing the snowball / Mass of Ann
b) To find Billy's velocity, we can use a similar approach:
Total momentum before throwing the snowball = Total momentum after throwing the snowball
The momentum of Ann and the snowball before throwing should be equal to the momentum of Billy after catching the snowball:
Momentum of Billy after catching the snowball = Momentum of Ann before throwing the snowball + Momentum of the snowball
Substituting the values, we get:
Momentum of Billy after catching the snowball = (66.1 kg x 2.29 m/s) + (0.0460 kg x 31.7 m/s)
Now, we divide the resulting momentum by Billy's mass to find his velocity:
Velocity of Billy after catching the snowball = Momentum of Billy after catching the snowball / Mass of Billy