Question

A person walking at some speed finds the rain falling vertically. If he doubles his speed the rain appears to fall at an angle 45 degrees to the vertical. At which angle will the rain appear to fall if he triples his speed

Answer 1

Given:

When the person walks with speed v, rain falls vertically

When he walks with 2v, the rain falls at an angle of 45° to the vertical

To find:

At what angle will the rain appears to fall when the person walks with 3v.

Solution:

We have considered the initial speed of the person to be v m/s in the horizontal direction and 0 m/s in vertical direction..

Let the Rain's horizontal velocity = Vx

Let the Rain's vertical velocity = Vy

Case 1 when the person walks at some speed finds the rain falling vertically

V - Vx = 0

V = Vx

Case 2 when he doubles his speed the rain appears to fall at an angle 45° to the vertical.

Horizontal velocity = 2V - Vx  =  2Vx - Vx  = Vx

Vertical Velocity = Vy

Angle = 45°

Therefore, Vx = Vy

Case 3 when he triples his speed  = 3V  = 3Vx

Horizontal velocity = 3Vx - Vx = 2Vx

Vertical Velocity = Vy = Vx

Let the Angle with Vertical = α

=> Tan α = 2Vx / Vx

=> α =  Tan⁻¹(2)

=>  α = 63.43°

Therefore the angle of the rain with the vertical will be 63.43°.