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An open merry go round rotates at an ang...

An open merry go round rotates at an angular velocity `omega`.A person stands in it at a distance `r` from the rotational axis.It is raining and the rain drops falls vertically at a velocity `v_(0)`.How should the person hold an umbrella to prorect himself from the rain in the best way.Angle made by umbrealla with the vertical is

A

`cot alpha=v_(0)/(romega)`

B

`tan alpha=v_(0)/(romega)`

C

`cot alpha=(romega)/v_(0)`

D

`tan alpha=v_(0)/(romega)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let th velocity of the drops above the person `rel.` to the merry go round be at angle `alpha` to the vertical. This angle can be determined from the velocity triangle `v_(0)=v_(rel)+v_(m.g.r)`,
`v_(rel)=v_(0)-v_(m.g.r)=(romega),cot alpha=v_(0)/(romega)`.
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An open merry-go-round rotates at an angular velocity omega . A person stands in it at a distance r from the rotational axis. It is raining, and the raindrops fall vertically at a velocity v_(0) . How should the person hold an umbrella to protect himself from the rain in teh best way ?

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?

Knowledge Check

  • If rain falls vertically with a velocity V_r and wind blows with a velocity V_w from east to west, then a person standing on the roadside should hold the umbrella in the direction

    A
    `tan theta = V_w/V_r`
    B
    `tan theta =V_r / V_w`
    C
    `tan theta =V_(rw)/sqrt(V_r^2+V_w^2)`
    D
    `tan theta =V_(r)/sqrt(V_r^2+V_w^2)`

  • A man is going due east with a velocity of 5ms^(-1) .It is vertically rainging downwards with a velocity of 4ms^(-1) .At what angle should he hold the umbrella to the vertical so as to protect him self from the rain?

    A
    `tan^(-1)(5/4)` in anti-clockwise direction
    B
    `tan^(-1)(5/4)` in clockwise direction
    C
    `tan^(-1)(5/4)`North of East
    D
    `tan^(-1)(5/4)`East of North

  • 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 umbrealla at an angle theta to vertical. The tan theta=

    A
    `2/sqrt5`
    B
    `sqrt5/2`
    C
    `2/3`
    D
    `3/2`

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