Question

It is raining vertically downwards By how many times that a person should increase his velocity
in order to change his umbrella position from an angle 30 with vertical to 60 with vertical to
protect himself from rain
1)1
2)2
3)3
4)2.5​

Answer 1

hey mate...

here is your answer...

Answer is (3) 3

refer to the attachment...

hope it helps...

Answer 2

Answer:

The man should increase his velocity by 3 times.

Explanation:

In order to answer this question we have to first understand why the man would have to change his umbrella angle from 30° (initial) to 60° (after increasing his velocity).

It is given in the question that the velocity of rain with respect to the ground is downwards (constant).

But,

Velocity of rain with respect to the man

$=velocity \: of \: rain - velocity \: of \: man$

Now the question states that,

Initially due to velocity of rain with respect to the man, the man had to hold the umbrella at 30°.

After the man increased is velocity he had to hold the umbrella at 60°.

Step-by-step solution:

Initial angle of the umbrella 30°

So,

90°- 30° = 60°

$\tan60 = \frac{velocity \: of \: rain}{x}$

$\sqrt{3} = \frac{velocity \: of \: rain}{x(initial \: velocity \: of \: man)}$

$velocity \: of \: rain = x \times \sqrt{3}$

When the umbrella angle is changed to 60°

So,

90°- 60° = 30°

$\tan30 = \frac{velocity \: of \: rain}{new \: velocity \: of \: man}$

$\frac{1}{ \sqrt{3} } = \frac{velocity \: of \: rain}{new \: velocity \: of \: man}$

From the previous equation you can write,

$\frac{1}{ \sqrt{3} } = \frac{x \times \sqrt{3} }{new \: velocity \: of \: man}$

$new \: velocity \: of \: man = x \times \sqrt{3} \: \times \sqrt{3}$

$new \: velocity \: of \: man =x \times ( \sqrt{3} ) ^{2}$

$new \: velocity \: of \: man = 3x$

Since, 'x' was the initial velocity of the man.

Therefore, the man increased his velocity by 3 times.