# physics

posted by .

Ricardo, mass 88 kg and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and symmetrically located with respect to the center of the canoe. Ricardo notices that the canoe moved 63.5 cm relative to a submerged log during the exchange and calculates Carmelita's mass, which she has not told him. What is it?

• physics -

mr..........|..............mc
mc..............|..........mr

The vertical bar | represents the centre of gravity of the masses of the two persons, mr for Ricardo, and mc for Carmelita.
When they exchange seats, they exert a force on the canoe in such a way that the heavier person pushes more on the canoe. The centre-of gravity (in theory) remains at the same place.

Therefore (3 - 0.635)/2=1.1825 is the location of centre of gravity from Ricardo.
We have therefore:
mr*1.1825=mc*(3-1.8175)
mc=mr*1.1825/1.8175
=57.25 kg

Check my thinking.

• physics -

so