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Question

# A boat can go at a speed 40 km/h in still water. If this boat is crossing a river when the speed of current is 20√3 km/h and the width of the river is 4 km, how long will the boat take to cross the river at a point directly opposite to starting point?

A
15 minutes
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B
1 hour
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C
20 minutes
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D
12 minutes
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Solution

## The correct option is D 12 minutes When the boat starts moving in the river, the velocity of the river pushes the boat towards the right. Hence the boat should make an angle θ towards the left of the vertical, so that it reaches the exact opposite point to the point of start. For the drift to be zero, the magnitude of x component of the velocity of the boat w.r.t. river should be equal to the magnitude of velocity of the river. Hence, 40sinθ=20√3⇒θ=60∘ Hence y component of the velocity vy=vbcos60o. Time taken by boat to cross the river =t=s(vb cos60o) s=width of river=4 km vb=40 km/ht=4(40 cos60o)=15 h=12 minutes Hence the correct option is (d).

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