A lumberjack (mass = 91.6 kg) is standing at rest on one end of a floating log (

Question

A lumberjack (mass = 91.6 kg) is standing at rest on one end of a floating log (mass = 224 kg) that is also at rest. The lumberjack runs to the other end of the log, attaining a velocity of +3.17 m/s relative to the shore, and then hops onto an identical floating log that is initially at rest. Neglect any friction and resistance between the logs and the water. (a) What is the velocity of the first log (again relative to the shore) just before the lumberjack jumps off? (b) Determine the velocity of the second log (again relative to the shore) if the lumberjack comes to rest relative to the second log.

Explanation / Answer

Answer:  lumberjack will be m and v. log will be M and V.

a) conservation of momentum
mv(i) + MV(i) = mv(f) +MV(f) since the beginnig velocity of both of them is zero so
0 = 99.7(4.74) +246V(f)
V(f) = -1.92 m/s

b) again concervation of momentum
mv(i) + MV(i) = (m + M)v(f)
99.7(4.74) + 246(0) = (99.7+246)v(f)
v(f) = +1.36 m/s

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