A child in danger of drowning in a river is being carried downstream by a curren

Question

A child in danger of drowning in a river is being carried downstream by a current that flows
uniformly with a speed of 2.5 km/h. The child is .6 km from shore and .8 km upstream of a boat
landing when a rescue boat leaves the landing to rescue the child. The boat is able to proceed at a
maximum speed of 20 km/h with respect to the water.
(a) At what angle with respect to the shore should the axis of the boat be set ?
(b) At what angle with respect to the shore will the resultant velocity of the boat be ?
(c) How long will it take to reach the child


please make steps clear

Explanation / Answer

a)in the frame of water, the boat can run at speed of 20km/h and the child ll stand still. (tan alpha = 0.8/0.6 so alpha=53 so angle is 90-53=37). so 37 degrees b) v_ver=20*sin53-2.5=13.5(km/h). v_hor=20*cos53=12(km/h). so that tan 0 = 1.125 so the angle=48.4. so its should be 90-48.4=41.6(degrees). C) T=sqrt(0.6^2+0.8^2)/20=0.05(h)

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