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Question

A stationary person observes that rain is falling vertically downwards at 30 km/h . A cyclist is moving up on an inclined plane making an angle of 30∘ with horizontal at 10 km/h . In which direction should the cyclist hold his umbrella to prevent himself from the rain?

A
At an angle tan1(335) with the inclined plane.
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B

At an angle tan1(335) with the horizontal.
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C

At an angle tan1(37) with the inclined plane.
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D

At an angle tan1(37) with the vertical.
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Solution

The correct option is D At an angle tan−1(√37) with the vertical.→vr=−30^j,→vm=10√32^i+102^j →vr/m=→vr−→vm=−5√3^i−35^j tanθ=5√335=√37⇒θ=tan−1(√37) with vertical Angle of vr/m with inclined plane is 60−θ=β tanβ=tan(60−θ)=tan60∘−tanθ1+tan60∘×tanθ=√3−√3/71+√3×√3/7=3√35 β=tan−1(3√35)

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