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Q.

A stationary person observes that rain is falling vertically down at 30 kmh-1. A cyclist is moving up on an inclined plane making an angle 30o with horizontal at 10 kmh-1. In which direction should the cyclist hold his umbrella to prevent himself from the rain?

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a

At an angle tan−1⁡335 with inclined plane

b

At an angle tan−1⁡335 with horizontal

c

At an angle tan−1⁡37with inclined plane

d

At an angle tan−1⁡37 with vertical

answer is A.

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Detailed Solution

v→r=−30j^,v→m=1032i^+102j^tan⁡θ=5335=37⇒θ=tan−1⁡37 with vertical Angle of vr/m with inclined plane is 60∘−θ=βtan⁡β=tan⁡60∘−θ     =tan⁡60∘−tan⁡θ1+tan⁡60∘tan⁡θ     =3−3/71+3⋅3/7=335⇒ β=tan−1⁡335
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