Question

A lumberjack (mass = 98 kg) is standing at rest on one end of a floating log (mass = 275 kg) that is also at rest. The lumberjack runs to the other end of the log, attaining a velocity of +3.5 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 just before the lumberjack jumps off? (Indicate the direction of the velocity by the sign of your answers.) m/s

(b) Determine the velocity of the second log if the lumberjack comes to rest on it.

Answer 1

let m1 = 98 kg
v1 = 3.5 m/s
m2 = 275 kg

a) Apply conservation of momentum while jumping

final momentum = initial momentum

m1*v1 + m2*v2 = 0

98*3.5 + 275*v2 = 0

v2 = -98*3.5/275

= -1.247 m/s   <<<<<<<<---------------Answer

b) Apply conservation of momentum after jumping on to other log

final momentum = initial momentum

(m1 + m2)*v = m1*v1

v = m1*v1/(m1 + m2)

= 98*3.5/(98 + 275)

= 0.9196 m/s <<<<<<<<---------------Answer