Question

A man holds an umbrella at 30° vertically to keep himself dry. He, then, runs at a speed of 10 ms^-1 and finds the raindrops to be hitting vertically. Speed of the raindrops w.r.t. earth and w.r.t. man are

• A. 20 ms^-1, 10 ms^-1
• B. 10ms^-1, 20$\sqrt{3}$ms^-1
• C. 10$\sqrt{3}$ms^-1, 20 ms^-1
• D. 20 ms^-1, 10$\sqrt{3}$ ms^-1.

Answer 1

Answer: (C)

10$\sqrt{3}$ms^-1, 20 ms^-1

Answer 2

Velocity of man |$\overrightarrow{v}$m| = 10 ms^-1. Using sin 30⁰ = v_m/v_re

vm = velocity of man v_re = velocity of rain w.r.t. earth

v_rm = velocity of rain w.r.t man

or v_re = v_m/sin30 = $\frac{10}{1/2}$ = 20 ms^-1

Again cos 30⁰ = v_rm/v_re

or v_rm = v_re cos 30

= 20 × $\frac{\sqrt{3}}{2}$ = 10$\sqrt{3}$ ms^-1