Browse Questions

# A boy is riding a cycle with a speed of $5\sqrt3$m/s towards east along a straight line.It starts raining with a speed of 15m/s in the vertical direction.What is the direction of rainfall as seen by the boy.

$\begin{array}{1 1}30^{\large\circ}\\20^{\large\circ}\\10^{\large\circ}\\50^{\large\circ}\end{array}$

Answer : $30^{\large\circ}$
Let us denote Earth, boy and rain with symbols A, B and C respectively. The question here provides the velocity of B and C with respect to A (Earth).
We need to determine the direction of rain (C) with respect to boy (B)
For the boy(B),the rain appears to fall,making an angle $"\theta"$ with the vertical (-y direction).
$\Rightarrow \tan\theta=\large\frac{V_{BA}}{V_{CA}}$
$\Rightarrow \large\frac{5\sqrt 3}{15}$
$\Rightarrow \large\frac{1}{\sqrt 3}$
$\Rightarrow \tan\theta=\tan 30^{\large\circ}$
$\theta=30^{\large\circ}$