First slide

Projection Under uniform Acceleration

Question

Rain is falling vertically with a velocity of 25 m $s^{- 1}$ . A woman rides a bicycle with a speed of 10 m $s^{- 1}$ in the north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to safe herself from rain?

Moderate

A

$t a n^{- 1} (0.4)$
B

$t a n^{- 1} (1)$
C

$t a n^{- 1} (\sqrt{3})$
D

$t a n^{- 1} (2.6)$

Solution

Here, $v_{R}$ = 25 m $s^{- 1}$ , $v_{w}$ = 10 m $s^{- 1}$
Velocity of rain w.r.t. woman :
Let $\frac{v_{R}}{v_{w}}$ make an angle $θ$ with vertical
$\tan θ = \frac{v_{W}}{v_{R}} = \frac{10}{2.5} = 0.4$
She should hold her umbrella at an angle of $θ$ = $\tan^{- 1}$ (0.4) with the vertical towards south.

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