# Relative Velocity (Man walking in rain question)

• kipup123
In summary, the conversation discusses the direction in which a cyclist should hold their umbrella to prevent themselves from the rain. The solution involves using the triangle law to find the velocity of rain with respect to the man, and taking into account the man's motion. The answer is given as tan^-1(3), which is determined by measuring the perpendicular in the rain-velocity vector and the angle from the horizontal direction. However, if the question is about the angle from the vertical direction, the answer may be different.

## Homework Statement

A stationary person observes that rain is falling vertically down at 30km/hr. A cyclist is moving on the level road, at 10km/hr. In which direction the cyclist should hold his umbrella to prevent himself from the rain?

2. The attempt at a solution
I used triangle law to find Velocity of rain with respect to man. The angle which comes up is tan^-1 (1/3), but the answer given is tan^-1(3). Where did I go wrong?

Thanks.

kipup123 said:
I used triangle law to find Velocity of rain with respect to man. The angle which comes up is tan^-1 (1/3), but the answer given is tan^-1(3). Where did I go wrong?

well, when the cyclist is static he will hold the umbrella vertical ; when he is moving he will tilt the umbrella to an angle from the vertical , therefore tan (angle) = perpendicular/base ; so check in your velocity diagram if the answer is , as you are quoting - it must be measuring perpendicular in the rain-velocity vector whose magnitude is 30 km/h then it may be measuring angle from horizontal direction.

kipup123 said:
In your diagram the reverse velocity vector of man will be applied to the rain as well as man separately..
then man will become static and he will observe rain drops which will have two velocities one acting towards left and another vertically downward so resultant will be a velocity completing the upper triangle- now the direction of this resultant making an angle with the horizontal is the direction in which the umbrella could be kept.
In this way one can see how the answer came into Tan^-1(3). comes up.
Your velocity diagram is to be corrected
If however some body asks -at what angle from vertical direction the umbrella should be kept -then the resultant is making an angle 90- previous calculation angle ...then your answer may have been correct.

kipup123
Thanks for the help.

drvrm

## 1. What is relative velocity?

Relative velocity is the measurement of the speed and direction of an object with respect to another object. It takes into account the movement of both objects and is affected by their relative positions and velocities.

## 2. How does relative velocity apply to the "Man walking in rain" question?

In the "Man walking in rain" question, relative velocity refers to the perceived speed and direction of the raindrops as seen by the man walking. The man's own velocity and direction of movement will affect how fast the raindrops appear to be falling on him.

## 3. What factors affect relative velocity in the "Man walking in rain" scenario?

The factors that affect relative velocity in this scenario include the speed and direction of the man's walking, the speed and direction of the rain, and the angle at which the rain is falling in relation to the man's movement.

## 4. How can relative velocity be calculated in the "Man walking in rain" question?

The relative velocity in this scenario can be calculated using vector addition. The velocity of the man and the velocity of the raindrops are added together to determine the overall velocity of the raindrops as seen by the man.

## 5. Why is understanding relative velocity important in science?

Understanding relative velocity is important in science because it helps us understand and predict the movement of objects in relation to each other. It is also a key concept in fields such as mechanics, astronomy, and fluid dynamics.