Question

If rain is falling at some angle from vertical and has horizontal velocity 2 m/s in east direction. With what velocity a man must move on the horizontal surface so that rain will appear vertical to him :​

Answer 1

Answer:

Man velocity is $2$ $m/sec$  towards the West direction.

Explanation:

• The relative velocity of an object with respect to a frame is calculated by keeping the other frame at rest.
• Relative velocity is the difference of velocity vectors.

The formula for relative velocity is:

$V_{RM} =V_{R}-V_{M}$

where, $V_{RM}$  is the man velocity relative to rain.

            $V_{R}$  is the rain velocity relative to the ground.

            $V_{M}$  is the man velocity relative to the ground.

Step 1:

Here, horizontal rain velocity is $2$ $m/s$  towards the east.

So,  $V_{R} =(2i - Yj)$ $m/s$

where $Y$ is the vertical component of rain velocity.

Step 2:

Applying the above formula:

$V_{RM} =(2 - V_{m})i - Yj$

To appear to the man that the rain is falling vertically, the horizontal component should cancel out.

So, $V_{m} = 2$ $m/sec$   towards the West direction.

Hence, man velocity is $2$ $m/sec$  towards the West direction.