Problem

A man walks at 5 km/h in the direction of a 20-km/h wind. If raindrops fall vertically a...

A man walks at 5 km/h in the direction of a 20-km/h wind. If raindrops fall vertically at 7 km/h in still air, determine the direction in which the drops appear to fall with respect to the man. Assume the horizontal speed of the raindrops is equal to that of the wind.

Step-by-Step Solution

Solution 1

Calculate the velocity of the rain using the following relation.

Here, is the velocity of the rain, is the velocity of the wind, and is the velocity of the rain with respect to the wind.

Substitute for and for .

…… (1)

Calculate the velocity of the rain using the following relation.

Here, is the velocity of the rain, is the velocity of the man, and is the velocity of the rain with respect to the man.

Substitute for .

…… (2)

Equate (1) and (2), we get

Calculate the magnitude of the relative velocity.

Therefore, the magnitude of relative velocity of rain with respect to man is

.

Calculate the direction in which the drops appear to fall with respect to the man.

Therefore, the direction in which the rain drops appear to fall with respect to the man is

.

Add your Solution
Textbook Solutions and Answers Search