Final answer:
Using conservation of momentum, the log moves 1.0 m relative to the shore as Ernie walks 3.0 m to reach Burt. No external horizontal forces are acting on the system, so Ernie's movement causes the log to move in the opposite direction to preserve the system's total momentum.
Step-by-step explanation:
The student's question concerns the movement of a log with two people on it, one walking towards the other. We can use the conservation of momentum principle to answer this question, since there are no external horizontal forces acting on the system of Ernie, Burt, and the log.
In the initial state, the total momentum of the system is zero because they are at rest. As Ernie walks towards Burt, the log moves in the opposite direction to conserve momentum. Let's denote Ernie's displacement towards Burt as x and the log's displacement in the opposite direction as d. The momentum conservation equation for this system will be:
Ernie's momentum change = - Log's momentum change
(40.0 kg)(x) = - (20.0 kg)(d)
Because Ernie has moved the entire length of the log (3.0 m), we set x to 3.0 m, making our equation:
(40.0 kg)(3.0 m) = - (20.0 kg)(d)
120.0 kg·m = - (20.0 kg)(d)
d = - 6.0 m
However, this negative sign only indicates that the log's direction of movement is opposite to Ernie's. The log has moved 6.0 m relative to Ernie, but relative to the shore, the distances will be in the same ratio as their masses. Since the total length that can be covered by the log and Ernie combined is 3.0 m, the log will move a distance of:
d relative to shore = (20.0 kg / (40.0 kg + 20.0 kg)) × 3.0 m
d relative to shore = (1/3) × 3.0 m
d relative to shore = 1.0 m
The log moves 1.0 m relative to the shore while Ernie walks the 3.0 m length of the log to reach Burt.