Question

A standing man observes rain falling vertically with a velocity 20m/s at an angle 30degree with the vertical?
1.Find the velocity with which the man should mode so that rain appears to fall vertically to him.
2. Now if he further increases his speed rainagain appears to fall at 30degree with the vertical.Find his new velocity.​

Answer 1

Answer:

10 m/s

20 m/s

Explanation:

A standing man observes rain falling vertically with a velocity 20m/s at an angle 30degree with the vertical?

1.Find the velocity with which the man should mode so that rain appears to fall vertically to him.

2. Now if he further increases his speed rainagain appears to fall at 30degree with the vertical.Find his new velocity.​

Rain falling vertically with a velocity 20m/s at an angle 30° with the vertical

Rain Horizontal Speed = 20Sin30° = 20 * 1/2 = 10 m/s

he velocity with which the man should mode so that rain appears to fall vertically to him = 10 m/s  in the direction of angle of Rain

if he further increases his speed rain again appears to fall at 30°

but in opposite

=> Horizontal Speed of Rain appearing = 20Sin(-30) = -10 m/s

Actual Horizontal Speed of Rain = 10 m/s

=> Man Speed = 10-(-10)  = 20 m/s

Answer 2

Answer:

(1). The velocity of man is 10 m/s.

(2). The new velocity of man is 20 m/s.

Explanation:

Given that,

Vertical velocity = 20 m/s

Angle = 30°

(1). The speed should a man run horizontally

So, that rain appears to him to be falling vertically

The horizontal speed  of the man should be

$v'=v\sin\theta$

Put the value into the formula

$v'=20\times\sin30$

$v'=10\ m/s$  

(2). If he further increases his speed rain again appears to fall at 30° with the vertical

The new horizontal velocity $v_{n}= +20\sin30$

The old horizontal velocity $v_{o}=-20\sin30$

New velocity of man = change in horizontal velocity of rain

$v_{m}=v_{n}-v_{o}$

Put the value into the formula

$v_{m}=20\sin30-(-20\sin30)$

$v_{m}=20\ m/s$

Hence, (I). The velocity of man is 10 m/s.

(II). The new velocity of man is 20 m/s.