Amy(mass 60kg) and Bob(mass 90kg) have gone fishing together. They find a good s

Question

Amy(mass 60kg) and Bob(mass 90kg) have gone fishing together. They find a good spot and they at the center of the canoe next to a stationary lilypad, which will serve the reference point x=o. The canoe is 4m long and has a mass of 40kg. Everything begins at rest. This means that the initial total momentum of the system is 0. Also since the canoe is uniform, its center of mass is at its geometric center. Because Amy and Bob begin at x=0, the center of mass of the system also begins at x=0. At some point, Amy gets sick of sitting next to Bob, so she walks at .5m/s toward the left end of the canoe. Bob remains seated. Assume water's resistive force is negligible. a) which direction will the canoe begin to move and how fast will they go? b) what type of force is responsible for causing the canoe to accelerate up to that speed? c) Amy sits down at the left end of the canoe and stops moving. Does the canoe continue moving? d) Because there were no external forces, the center of mass of the system must still be located at its original position. Use this fact to determice the final positions Xa and Xb of Amy and Bob relatice to the stationary lilypad. e) who ends up closer to the lilypad? Briefly explain

Explanation / Answer

a) the canoe will move in the direction opposite to that of amy.

let the speed of the canoe be v.

so speed oa my relative to canoe=0.5 m/s

so, conserving momentum,

60*(5-v)=(80+40)*v

or v=1.667 m/s

b)the force exerted by any;s legs are responsible for it

c)no it stops moving once amy stops moving.

let the distance moved by the canoe be x.so,

60*(4-x)=(80+40)*x

or x=1.33 m

so distance of amy from the lilypad=4-1.33

=2.67 m

distance of bob=1.33 m

e)bob ends up being closed to the lilypad since he is heavier than amy

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