Question

A nab running on a horizontal road at 8 ms^-1 finds rain falling vertically. If he increase his speed to 12 ms^-1, he finds that drops make 30^o angle with the vertical. Find velocity of rain with respect to the road.

• A. 4$\sqrt{7}$ ms^-1
• B. 8$\sqrt{2}$ms^-1
• C. 7$\sqrt{3}$ms^-1
• D. 8 ms^-1

Answer 1

Answer: (A)

4$\sqrt{7}$ ms^-1

Answer 2

V_m = (V_rx - V_m)$\widehat{i}$ + V_ry$\widehat{j}$

case (i) tan 90 = $\frac{V_{ry}}{V_{rx} - V_{m}} = \frac{V_{ry}}{V_{rx} - 8}$ or V_rx = 8 ms^-1

case (ii) tan 30 = $\frac{V_{rx} - V_{m}}{V_{ry}} = \frac{8 - 12}{V_{ry}}$ or V_ry= - 4√3 ms^-1

V_r = $8\widehat{i} - 4\sqrt{3}\widehat{j} = 4\sqrt{2^{2} + 3} = 4\sqrt{7}ms^{- 1}$

tan θ = $\frac{V_{ry}}{V_{rx}} = \frac{4\sqrt{3}}{8} = \frac{\sqrt{3}}{2}$

θ = tan^-1$\frac{\sqrt{3}}{2}$ with respect to road (horizontally).