Home
Class 11
PHYSICS
A man is coming down an incline of angle...

A man is coming down an incline of angle `30^@`. When he walks with speed `2(sqrt(3)) m s^-1` he has to keep his umbrella vertical to protect himself from rain. The actual speed of rain is `5 ms^-1`. At angle with vertical should he keep his umbrella when he is at rest so that he does not getb drenched ?
.

Text Solution

Verified by Experts

Velocity of rain w.r.t man
`vec v_(r,m) = x hat j = vec v_r - vec v_m`
`vec v_m = 2 sqrt(3) [cos 30 hat i + sin 30 hat j]`
=`3 hat I + sqrt(3) hat j`
`vec v_r = -3 hat i + (x - sqrt(3)) hat j`
`5 = sqrt(3^2 + (x - sqrt(3))^2)`
`16 = (x - sqrt(3))2 rArr 4 + sqrt(3) = x`
`vec v_r = - 3 hat i + 4 hat j`
`tan theta = (3)/(4) rArr theta = 37^@`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • KINEMATICS-2

    CENGAGE PHYSICS ENGLISH|Exercise Solved Examples|7 Videos

  • KINEMATICS-2

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 5.1|15 Videos

  • KINEMATICS-1

    CENGAGE PHYSICS ENGLISH|Exercise Integer|9 Videos

  • KINETIC THEORY OF GASES

    CENGAGE PHYSICS ENGLISH|Exercise Compression|2 Videos

Similar Questions

Explore conceptually related problems

To a man going with a speed of 5 ms^-1 , rain appears to be falling vertically. If the actual speed of rain is 10 m s^-1 , then what is the angle made by rain with the vertical ?

Rain is falling vertically. A man running on the road keeps his umbrella tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them keep their umbrella vertical to avoid the vertical sun-rays. Explain.

Rain is falling vertically with velocity 10m /s and a man is moving with velocity 6 m s^-1 . Find the angle at which the man should hold his umbrella to above getting wet.

The rowing speed of a man relative to water is 5 kmh^(-1) and the speed of water flow is 3 kmh^(-1) . At angle to the river flow should he head if he wants to reach a point on the other bank, directly opposite to starting point ?

When it is raining vertically down, to a man walking on road the velocity of rain appears to be 1.5 times his velocity. To protect himself from rain he should hold the umbrella at an angle theta to vertical. Then tan theta=

Rain is falling vertically with a speed of 20ms^(-1) ., A person is running in the rain with a velocity of 5 ms^(-1) and a wind is also blowing with a speed of 15 ms^(-1) (both from the west) The angle with the vertical at which the person should hold his umbrella so that he may not get drenched is:

A boy is running on a horizontal road with a velocity of 5 m/s. At what angle should he hold his umbrella in order to protect him self from the rain if the rain is falling vertically with a velocity of 10 m/s?

A person walking at 4 m/s finds rain drops falling slantwise into his face with a speed of 4 m/s at an angle of 30^(@) with the vertical . Show that the actual speed of the rain drops is 4 m/s .

It is raining at a speed of 5 ms^(-1) at an angle 37^@ to vertical, towards east. A man is moving to west with a velocity of 5 ms^(-1) . The angle with the vertical at which he has to hold the umbrella to protect himself from rain is

Statement -1 : A man standing on the ground has to hold his umbrella at an angle theta with the vertical to protect himself from rain. It is possible that the man now starts running on the ground with certain speed, but he still has to hold his umbrella at angle theta with the vertical to protect himself from rain. Statement -2 : Vertical component of velocity of rain w.r.t man does not change. if he starts running on a horizontal ground.

Home
Profile