A 61.7 kg canoeist stands in the middle of her canoe. The canoe is 3.9 m long, and the end that is closest?

Question

A 61.7 kg canoeist stands in the middle of her canoe. The canoe is 3.9 m long, and the end that is closest to land is 2.5 m from the shore. The canoeist now walks toward the shore until she comes to the end of the canoe. Suppose the canoeist is 3.4 m from shore when she reaches the end of her canoe. What is the canoe's mass?

Is there a simple way to do this problem? I can not seem to figure it out.

Answer 1

This can be modeled by the center of mass staying in a constant location.

If we take 0 as the shore, the center of mass at the start is
2.5+3.9/2, since she is standing in the middle of the canoe.

After the stroll, she is 3.4 m from shore. Her mass is 61.7 kg
Since the canoe is 3.9 m log, the center of the canoe is
3.4 +3.9/2 from shore

so set up the equations:

(2.5+3.9/2)*(61.7+mc)
where mc is the mass of the canoe
this now must equal

3.4*61.7+mc*(3.4 +3.9/2)

(2.5+3.9/2)*mc+
(2.5+3.9/2)*(61.7)
=3.4*61.7+mc*(3.4 +3.9/2)

(3.4-2.5)mc=
(2.5-3.4+3.9/2)*(61.7)

mc=(2.5-3.4+3.9/2)*(61.7)/
(3.4-2.5)

=72 kg

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