Question

A 45kg boy is holding a 12kg pumpkin while standing on ice skates on a smooth frozen pond. The boy tosses the pumpkin with a horizontal speed of 2.8m/s to a 37kg girl (also wearing ice skates) catches it. What are the final speeds of the boy and girl?

Answer 1

Girl `|v| = 0.69 m/s`

Boy `|v| = 0.75 m/s`

Explanation:

For the boy holding the pumpkin, initial momentum is 0. After tossing it, he will have momentum equal and opposite that of the pumpkin:

`0 = 12kg*2.8m/s + 45kg*v`
`-45kg*v = 33.6kg m/s`
`v = -0.747m/s`
`|v| = 0.75 m/s` <===the boy's final speed

For the girl, after catching the pumpkin she will have all the momentum the pumpkin had in flight:
`12kg*2.8m/s = (37kg + 12kg)*v`
`-33.6kg m/s = 49kg*v`
`v = -0.69 m/s`
`|v| = 0.69 m/s`<===the girl's final speed

Notice that both their momenta total to zero:
`45kg*0.75m/s = 49kg*0.69m/s`
`34 kg m/s = 34 kg m/s`

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