First slide

Relative motion in 2 dimension

Question

Aman walks horizontally in rain with a velocity of 5 m/s. The raindrops strike on his back at angle of 45⁰ with the horizontal. Then for the actual rain's velocity

Difficult

A

horizontal component = vertical component
B

horizontal component > vertical component
C

horizontal component < vertical component
D

none of these

Solution

Velocity of man: $\vec{v_{m}} = 5 \hat{i}$
Velocity of rain w.r.t man:
${\vec{v_{}}}_{r / m} = v_{1} \cos 45^{\circ} \hat{i} - v_{1} \sin 45^{\circ} \hat{k} = \frac{v_{1}}{\sqrt{2}} \hat{i} - \frac{v_{1}}{\sqrt{2}} \hat{k}$
Hence, velocity of rain:
$\begin{array}{l} \vec{v_{r}} = {\vec{v}}_{r / m} + \vec{v_{m}} \\ \Rightarrow \vec{v_{r}} = (\frac{v_{1}}{\sqrt{2}} + 5) \hat{i} - \frac{v_{1}}{\sqrt{2}} \hat{k} \end{array}$
Horizontal component of rain's velocity $= \frac{v_{1}}{\sqrt{2}} + 5$
Vertical component of rain's velocity $= \frac{v_{1}}{\sqrt{2}}$
So horizontal component > vertical component

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App