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° to the vertical. To what angle the rain will appear to fall
he triples his speed?​

Answer 1

Given : 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.

To Find : At which angle will the rain appear to fall if he triples his speed?

Solution:

Man Horizontal Velocity =  V  and Vertical Velocity = 0

Rain Horizontal Velocity = Vx

Rain Vertical Velocity = Vy

A person walking at some speed finds the rain falling vertically

=> V - Vx = 0

=> V = Vx

If he doubles his speed the rain appears to fall at an angle 45 degrees to the    vertical.

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

Vertical Velocity = Vy

Angle = 45°

=> Vx = Vy

triples his speed  = 3V  = 3Vx

Horizontal velocity = 3Vx - Vx = 2Vx

Vertical Velocity = Vy = Vx

Angle with Vertical = α

=> Tan α = 2Vx / Vx

=> α =  Tan⁻¹(2)

=>  α = 63.43°

63.43°   to the vertical.

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