Question

A man at rest observes that rain is falling with the
velocity of 20 m/s at an angle 30° with the vertical.
The velocity with which the man should move on a
horizontal road, such that rain again appears to fall
at 30° with the vertical, will be
(1) 20 m/s
(2) 20/3 m/s
(31 10 m/s
(4) 10/3 m/s​

Answer 1

Answer:

The velocity is 20 m/s.

(1) is correct option.

Explanation:

Given that,

Velocity = 20 m/s

Angle = 30°

We need to calculate the component

Horizontal component = v cosθ

$v=v\cos30$.....(I)

$v=v\times\dfrac{\sqrt{3}}{2}$

Vertical component = v sin θ

$v=v\sin30=v\times\dfrac{1}{2}$....(II)

When he begins to move with a velocity of 20 m/s then the drops appear with horizontal velocity

$v=\dfrac{v\sqrt{3}}{2}+20$

Divided equation equation (II) by (I)

$\tan\theta=\dfrac{\dfrac{v}{2}}{\dfrac{\sqrt{3}v}{2}+20}$

$\tan60=\dfrac{\dfrac{v}{2}}{\dfrac{\sqrt{3}v}{2}+20}$

$\sqrt{3}=\dfrac{\dfrac{v}{2}}{\dfrac{\sqrt{3}v}{2}+20}$

$\dfrac{3v}{2}+20=\dfrac{v}{2}$

$v=-20\ m/s$

Negative sign show the direction of rain.

Hence, The velocity is 20 m/s.