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 : 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.

Answer 2

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