Question

A 70.0-kg person throws a 0.0480-kg snowball forward with a ground speed of 33.5 m/s. A second person, with a mass of 55.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 3.90 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. (Take the direction the snowball is thrown to be the positive direction. Indicate the direction with the sign of your answer.)

Answer 1

The final velocity of the thrower is
`\bf{3.88~m/s}` and the final velocity of the catcher is
`\bf{0.029~m/s}`.

Step-by-step explanation:

Given:

The mass of the thrower,
`m_(t) = 70~Kg`.

The mass of the catcher,
`m_(c) = 55~Kg`.

The mass of the ball,
`m_(b) = 0.0480~Kg`.

Initial velocity of the thrower,
`v_(it) = 3.90~m/s`

Final velocity of the ball,
`v_(fb) = 33.5~m/s`

Initial velocity of the catcher,
`v_(ic) = 0~m/s`

Consider that the final velocity of the thrower is
`v_(ft)`. From the conservation of momentum,

`&& m_(t)v_(ft) + m_(b)v_(fb) = (m_(t) + m_(b))v_(it)\\&or,& v_(ft) = ((m_(t) + m_(b))v_(it) - m_(b)v_(fb))/(m_(t))\\&or,& v_(ft) = ((70 + 0.0480)(3.90) - (0.0480)(33.5))/(70)\\&or,& v_(ft) = 3.88~m/s`

Consider that the final velocity of the catcher is
`v_(fc)`. From the conservation of momentum,

`&& (m_(c) + m_(b))v_(fc) = m_(b)v_(it)\\&or,& v_(fc) = (m_(b)v_(it))/((m_(c) + m_(b)))\\&or,& v_(fc) = ((0.048)(33.5))/((55.0 + 0.0480))\\&or,& v_(fc) = 0.029~m/s`

Thus, the final velocity of thrower is
`3.88~m/s` and that for the catcher is
`0.029~m/s`.