A worker is poling a boat-a very efficient mode of transportation-across a shall

Question

A worker is poling a boat-a very efficient mode of transportation-across a shallow lake. He pushes parallel to the length of the light pole, exerting on the bottom of the lake a force of 235 N. Assume the pole lies in the vertical plane containing the boat's keel. At one moment, the pole makes an angle of 40.0° 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 360 kg.

(a) The water exerts a buoyant force vertically upward on the boat. Find the magnitude of this force.
___________ N

(b) Model the forces as constant over a short interval of time to find the velocity of the boat 0.200 s after the moment described.
____________ m/s

Explanation / Answer

Given Force exerted by the pole on the water is , Fp = 235 N at an angle 40^0 Fp is resolved into Fp cos? along x axis, and Fp sin? along yaxis The drag force , Fd = 47.5 N Mass of the boat, m = 360 kg a)Buoyant force exerted by the water vertically upward is equal to mg + Fsin? since the weight of the boat acts downwards                                Fb = mg + Fsin?                                    = 360 kg *9.8 m/s^2 + 235 N sin40                                    = 3679 N b) The net force acting on the boat is        F = Fp cos40 - Fd 360 kg a = 235 N cos 40 - 47.5 N       a = 0.36 m/s^2 The initial velocity ,vi =0.857 m/s Time interval, t = 0.2 s since a = (vf - vi)/t        0.36 m/s^2 = (vf -0.857 m/s)/0.2s           vf = 0.93 m/s is the velocity of the boat              

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