Show your work and include units with your answers for full credit. An empty can

Question

Show your work and include units with your answers for full credit. An empty canoe, mass mc = 25 kg, is floating away from a dock in calm water with a speed of vc = 0.80 m/s in the + x direction. When the canoe’s owner (mass mp = 75 kg) realizes this, he gets a running start of vp = 2.40 m/s in the + x direction and jumps into the canoe.

(a) What is the velocity of the canoe-person system just after he lands in the canoe? Indicate the direction with the sign of your answer. You may ignore frictional forces.

(b) What is the change in momentum of the canoe only during this “collision?” Be sure to include the correct sign.

(c) What is the change in momentum of the person only during this “collision?” Be sure to include the correct sign.

Explanation / Answer

a) applying momentum conservation,

mcvc + mpvp = (mc + mp)v

25 x 0.8 + 75 x 2.4 = 100v

v = 2 m/s in +x direction

b) change in momentum of canoe = mc(v - vc) = 25 x (2 - 0.8) = 30 kgm/s

c) change in momentum of person = mp(v - vp) = 75 x (2 - 2.4) = -30 kgm/s

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