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.

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# .
Let#v_b# be velocity of boy after tossing. Setting up the equation we get#12xx2.8 + 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#