A baseball player uses a pitching machine to help him improve his batting averag

Question

A baseball player uses a pitching machine to help him improve his batting average. He places the 51.0 kg machine on a frozen pond. The machine fires a 0.13 kg baseball horizontally at a speed of 44.6 m/s. a) What is (in kg m/s) the combined momentum of pitching machine and ball before the ball is fired? b) What is (in kg m/s) the combined momentum of pitching machine and ball after the ball is fired? c) What is (in kg m/s) the momentum of the baseball the moment it is fired? d) What is the magnitude of the recoil velocity of the machine? Answer in units of m/s.

Explanation / Answer

Use the conservation of momentum
as the machine and ball are initially at rest
mpvp = 0 = mmvm +mbvb

where mp is mass of machine plus ball or 51 kg
vp is initial velocity of the system which is zero.
mm is mass of machine after ball is thrown
vm is machine velocity after ball is thrown
mb is mass of ball
vb is velocity of thrown ball

solving for vm
0 = mmvm +mbvb
-mbvb = mmvm
vm = -mbvb/mm
vm = -(0.13)(44.6)/(51 - 0.13)

vm = -0.114 m/s

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