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Relative Motion in 1D

Rain is falli...

Question

Rain is falling vertically with a speed of $35 m s^{- 1}$ . Winds start blowing after some time with a speed of $12 m s^{- 1}$ in an east to west direction. In which direction should a boy wait at a bus stop holding his umbrella?

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Solution

Speed of rain= $3 m / s$
Wind speed= $12 m / s$

$∣ ∣ \to A D ∣ ∣ = ∣ ∣ \to A B ∣ ∣ + ∣ ∣ \to A C ∣ ∣ A D = \sqrt{{(35)}^{2} + 12^{2}} = \sqrt{1225 + 44} = 37 tan θ = \frac{35}{12}, θ = 71$
Rain is falling at an angle of $71 °$ from horizontal.

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