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?
1 Answer
Apr 8, 2018
We need to use the Law of Conservation of Momentum.
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For the boy standing and holding the pumpkin. Initial momentum
=0 . In the absence of external force, after tossing the pumpkin total momentum of Boy+Pumpkin system must also be=0 .
Letv_b be velocity of boy after tossing. Setting up the equation we get12xx2.8 + 45xxv_b=0
=>v_b = -33.6/45
=>v_b = -0.74bar6\ ms^-1
Boy's final speed|v_b| = 0.75\ ms^-1 -
For the girl+pumpkin system. Initial momentum is of pumpkin only. After catching the pumpkin, girl+pumpkin system will have momentum equal to the initial momentum. Let
v_g be velocity of girl after catching.Therefore,12xx2.8 = (37 + 12)xxv_g
=>v_g= 33.6/49
=>v_g= 0.69\ ms^-1