Question

A man is moving with constant velocity v = 20m/s in
horizontal plane. A what angle to the horizontal should
the man hold his umbrella so that the can protect himself
from rain falling vertically with velocity 60m/sec.​

Answer 1

Given :

• Velocity of man = v₁ = 20 m/s
• Velocity of rain = v₂ = 60 m/s

To find :

• Angle at which the man should hold his umbrella to protect himself

Solution :

• Refer the diagram attached.
• Consider the man is stationary instead of moving ahead and the rain is moving towards him instead of vertically downwards.
• In the ΔABC, AB is the velocity of the rain and BC is the velocity of the man.
• If we consider the rain moving towards the man, he will have to hold the umbrella at the angle θ .
• tanθ = AB/BC

                 = 60 ÷ 20

     ∴ θ = tan⁻¹(3)

     ∴ θ = 71.565°

Answer : The man will have to hold his umbrella at an angle of 71.56° to the vertical to protect himself from the rain.