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Q.

A person walking at 4 m/s finds rain drops falling slant wise in to his face with a speed of 4m/s at an angle of 30^o with the vertical the actual speed of the rain drops is_____

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a

8 m/s

b

6 m/s

c

5 m/s

d

4 m/s

answer is A.

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Detailed Solution

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$\begin{array}{l} {\bar{V}}_{rp} = {\bar{V}}_{r} - {\bar{V}}_{p} \Rightarrow {\bar{V}}_{r} = {\bar{V}}_{rp} + {\bar{V}}_{p} \\ |{\bar{V}}_{r}| = \sqrt{V_{rp}^{2} + V_{p}^{2} + 2 V_{rp} V_{p} \cos θ} [∵ θ = 30^{0} + 90^{0} = 120^{0}] \\ = \sqrt{4^{2} + 4^{2} - 2 \times 4 \times 4 \times \frac{1}{2}} = 4 m / s \end{array}$

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