The figure below shows a worker poling a boat-a very efficient mode of transport

Question

The figure below shows a worker poling a boat-a very efficient mode of transportation-across a shallow lake. He pushes parallel to the length of the light pole, exerting a force of magnitude 245 N on the bottom of the lake. Assume the pole lies in the vertical plane containing the keel of the boat. At one moment, the pole makes an angle of 32.0 degree with the vertical and the water exerts a horizontal drag force of 47.5 N on the boat, opposite to its forward velocity of magnitude 0.857 m/s. The mass of the boat including its cargo and the worker is 395 kg. The water exerts a buoyant force vertically upward on the boat. Find the magnitude of this force. Model the forces as constant over a short interval of time to find the magnitude of the velocity of the boat 0.570 s after the moment described.

Explanation / Answer

here ,

a)

let the buyoant force is Fb

for the vertical equilibrium of boat

Fb + 245 * sin(32) = 395 * 9.8

Fb = 3736.4 N

the buyoant force is 3736.4 N

b)

Using seocnd law of motion

change in momentum = net force * time

395 * v = (245 * cos(32) - 47.5) * 0.57

v = 0.231 m/s

the velocity of boat is 0.231 m/s

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