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Question

A lorry with a vertical wind shield moves on a horizontal road in a rainstorm at a speed of 15 m/s. The rain drops fall vertically with a speed of 30 m/s. The angle at which the rain drops strike the wind shield for the driver is :

A
θ=tan123
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B
θ=tan112
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C
θ=tan113
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D
θ=tan114
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Solution

The correct option is B θ=tan112

As observed by the driver, the rain drops will strike the windshield in the direction of velocity of rain w.r.t lorry(vrl)

vrl=Velocity of rain w.r.t lorry
vrg=Velocity of rain w.r.t ground
vlg=Velocity of lorry w.r.t ground

Using equation for relative velocity,
vrg=vrl+vlg

From the vector triangle as shown in figure,

tanθ=|vlg||vrg|=1530=12

θ=tan112

Why this question?When rain drops are falling vertically w.r.t the ground,then they will appear to fall at an angle with respect to a moving observer due to addition of the velocity of observer in the velocity of rain w.r.t ground.

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