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.

  1. 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#

  2. 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#