A lorry with a vertical wind shield moves on a horizontal road in a rainstorm at a speed of 15m/s. The rain drops fall vertically with a speed of 30m/s. The angle at which the rain drops strike the wind shield for the driver is :
A
θ=tan−123
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B
θ=tan−112
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C
θ=tan−113
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D
θ=tan−114
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Solution
The correct option is Bθ=tan−112
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=tan−112
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.