Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A man sitting in a bus travelling in a direction from west to east with a speed of $40 \text{ km/h}$ observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear:

To fall vertically downwards

To fall at an angle going from west to east

To fall at an angle going from east to west

The information given is insufficient to decide the direction of the rain

Step-by-Step Solution

Relative Velocity Equation: Let $\mathbf{v}_r$ be the velocity of rain w.r.t. ground, $\mathbf{v}_b$ be the velocity of the bus w.r.t. ground, and $\mathbf{v}_{rb}$ be the velocity of rain w.r.t. the bus. The relationship is $\mathbf{v}_{rb} = \mathbf{v}_r - \mathbf{v}_b$ or $\mathbf{v}_r = \mathbf{v}_{rb} + \mathbf{v}_b$ .
Given Conditions: The bus moves West to East: $\mathbf{v}_b = v \hat{i}$ (where $\hat{i}$ is unit vector towards East). The man in the bus observes rain falling vertically downwards: $\mathbf{v}_{rb} = -u \hat{j}$ (where $-\hat{j}$ is unit vector vertically downwards).
Vector Addition: Substituting these into the equation for $\mathbf{v}_r$ : $\mathbf{v}_r = -u \hat{j} + v \hat{i}$ .
Analysis: The velocity of rain w.r.t. the ground ( $\mathbf{v}_r$ ) has a vertical component downwards ( $-u \hat{j}$ ) and a horizontal component towards the East ( $+v \hat{i}$ ). Therefore, the rain falls at an angle deviating towards the East (going from West to East).

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