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 solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the exchange of the snowball should be equal to the total momentum after the exchange.
Let's break down the problem into two parts: Ann's initial velocity and Billy's initial velocity.
a) Ann's velocity:
Ann's initial velocity is 2.29 m/s. She throws a snowball with a ground speed of 31.7 m/s. The mass of Ann is 66.1 kg, and the mass of the snowball is 0.0460 kg.
Before the exchange, Ann's momentum is given by:
Momentum_initial_Ann = mass_Ann * velocity_Ann
Momentum_initial_Ann = 66.1 kg * 2.29 m/s
After the exchange, Ann's momentum is given by:
Momentum_final_Ann = (mass_Ann + mass_snowball) * velocity_final_Ann
Since we know that the total momentum before and after the exchange is the same, we can set up the equation:
Momentum_initial_Ann = Momentum_final_Ann
66.1 kg * 2.29 m/s = (66.1 kg + 0.0460 kg) * velocity_final_Ann
Now, we can solve for velocity_final_Ann.
b) Billy's velocity:
Billy is initially at rest, which means his initial velocity is 0 m/s. After the exchange, he catches the snowball, so his mass changes. The new mass of Billy after catching the snowball is (mass_Billy + mass_snowball).
The momentum of Billy after the exchange is given by:
Momentum_final_Billy = (mass_Billy + mass_snowball) * velocity_final_Billy
Again, using the principle of conservation of momentum:
Momentum_initial_Ann = Momentum_final_Billy
66.1 kg * 2.29 m/s = (mass_Billy + 0.0460 kg) * velocity_final_Billy
Now, we can solve for velocity_final_Billy.
By calculating the above equations, we can determine the final velocities of both Ann and Billy.