Answer :
Final answer:
The log moves in the opposite direction to the lumberjack due to conservation of momentum. With the lumberjack's mass and velocity known, the calculation shows the log's speed relative to the shore is 0.18 m/s, matching option b after rounding.
Explanation:
The conservation of momentum in a closed system. When the lumberjack jogs along the log, he exerts a force on the log, propelling it in the opposite direction to conserve momentum, since no external forces are acting on the system. As the lumberjack's mass is 94 kg and he moves with a velocity of 2.2 m/s relative to the shore, we can find the log's velocity relative to the shore using:
Conservation of momentum
:
initial total momentum = final total momentum
Let's assume that forward is positive. Then, before the lumberjack starts jogging, the total momentum of the system (lumberjack plus log) is zero because they are at rest:
Initial total momentum = 0
After the lumberjack starts jogging, the total momentum must still be zero:
Final total momentum = lumberjack's momentum + log's momentum
0 = (94 kg × 2.2 m/s) + (1200 kg × log's velocity)
0 = 206.8 kg·m/s + (1200 kg × log's velocity)
log's velocity = -206.8 kg·m/s / 1200 kg
log's velocity = -0.172 m/s
The negative sign indicates the log moves in the opposite direction to the lumberjack. Therefore, the correct choice for the log's speed relative to the shore is 0.18 m/s, which matches option b after rounding to two decimal places.
