65.0-kg person throws a .045kg snowball forward with a ground speed of 30.0 m/s. a second person with a mass of 60.0-kg catches the snowball. both people are on skates. the first person is intially moving forward wit ha speed of 2.50 m/s and the second person is initially at rest. what are the velocities of the two people after the snowball is exchanged? disregard the friction between the skates and the ice
To find the velocities of the two people after the snowball is exchanged, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the exchange must be equal to the total momentum after the exchange.
The formula for momentum is given by:
Momentum = mass × velocity
Let's calculate the initial momentum of the first person (person 1), the initial momentum of the second person (person 2), and the final momentum of the system.
Person 1:
Mass (m1) = 65.0 kg
Initial velocity (v1i) = 2.50 m/s
Momentum of person 1 (initial) = m1 × v1i = 65.0 kg × 2.50 m/s
Person 2:
Mass (m2) = 60.0 kg
Initial velocity (v2i) = 0 m/s (at rest)
Momentum of person 2 (initial) = m2 × v2i = 60.0 kg × 0 m/s
Snowball:
Mass (ms) = 0.045 kg
Velocity (vs) = 30.0 m/s
Momentum of the snowball = ms × vs = 0.045 kg × 30.0 m/s
Total initial momentum = Momentum of person 1 (initial) + Momentum of person 2 (initial) + Momentum of the snowball
Now, since the total momentum before the exchange is equal to the total momentum after the exchange, we can set up the equation as follows:
Total initial momentum = Total final momentum
(m1 × v1i) + (m2 × v2i) + (ms × vs) = (m1 × v1f) + (m2 × v2f) + (ms × vf)
Now let's consider the final velocities of person 1 (v1f) and person 2 (v2f) after the snowball transfer. Since both people are on skates, the interaction between them is frictionless. Therefore, according to the law of conservation of momentum:
Total initial momentum = Total final momentum
(65.0 kg × 2.50 m/s) + (60.0 kg × 0 m/s) + (0.045 kg × 30.0 m/s) = (65.0 kg × v1f) + (60.0 kg × v2f) + (0.045 kg × vf)
Solving the equation allows us to find the final velocities of both people (v1f and v2f) and the snowball (vf).