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A boy is running on a horizontal road wi...

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?

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To solve the problem of determining the angle at which the boy should hold his umbrella to protect himself from the rain, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the velocities**: - The boy is running with a velocity \( v_b = 5 \, \text{m/s} \) horizontally. - The rain is falling vertically with a velocity \( v_r = 10 \, \text{m/s} \). ...
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A man walking on a road with a velocity of 5 km per hour encounters rain falling vertically with a velocity of 25 km per hour. At what angle should he holds his umbrella in order to protect himself form the rain?

By the term velocity of rain, we mean velocity with which raindrops fall relative to the ground. In absence of wind, raindrops fall vertically and in presence of wind raindrops fall obliqucly. Moreover raindrops acquire a constant terminal velocity due air resistance very quickly as they fall toward the carth. A moving man relative to himself observes an altered velocity of raindrops. Which is known as velocity of rain relative to the man. It is given by the following equation. vec(v)_(rm)=vec(v)_(r)-vec(v)_(m) A standstill man relative to himself observes rain falling with velocity, which is equal to velocity of the raindrops relative to the ground. To protect himself a man should his umbrella against velocity of raindrops relative to himself as shown in the following figure. Rain is falling vertically with velocity 80 cm/s. (a) How should you hold your umbrella ? (b) You start walking towards the east with velocity 60 cm/s. How should you hold umbrella ? (c) You are walking towards the west with velocity 60 cm/s. How should you hold your umbrella ? (d) You are walking towards the north with velocity 60 cm/s. How should you hold your umbrella? (e) You are walking towards the south with velocity 80 cm/s. How should you hold your umbrella ?

Knowledge Check

  • 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)`

  • A Person is walking in rain feels the velocity of rain as twice to his velocity.At which angle he should hold the umbrella with vertical if he moves forward, if it is raining vertically downwards

    A
    `30^(@)`
    B
    `45^(@)`
    C
    `60^(@)`
    D
    `90^(@)`

  • A car is moving on horizontal ground with a velocity vm s^(-1) with respect to earth. The driver of the car observes the rain to be falling vertically downwards with velocity 2vm s^(-1) . What is the velocity of the rain with respect to the driver ?

    A
    3v
    B
    `vsqrt(3)`
    C
    `vsqrt(5)`
    D
    none of these

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    A man is going in a topless car with a velocity of 10.8kmph."l It is raining vertically downwards.He has to hold the umbrella at angle 53^(0) to the vertical to protect himself from rain.The actual velocity of the rain is (cos53^(0)=(3)/(5))

    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.

    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?

    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.

    A person is standing on road by holding an umbrella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10 m/s, when the velocity of wind is zero. Suddenly wind begins to flow at a speed of 20m/s, 30^(@) south of west. Now by what angle the person has to rotate his umbrella in order to protect himself from rain ?

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