A man sitting in a bus travelling in a direction from west to east with a speed of $40 ext{ km/h}$ observes

Question

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

Accepted Answer

1.  **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 $\mathbf{v}_r = \mathbf{v}_{rb} + \mathbf{v}_b$ .
2.  **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).
3.  **Vector Addition:** Substituting these into the equation for $\mathbf{v}_r$:
    $\mathbf{v}_r = -u \hat{j} + v \hat{i}$.
4.  **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).

Step-by-Step Solution

Practice All PHYSICS Questions