Question

rain appears to be falling at an angle of 370 with vertical to the driver of a car moving with a velocity of 7 m/s. when he increases the velocity of the car to 25 m/s, the rain appear again to fall at an angle 370 with vertical. what is the actual velocity of rain and it's direction with vertical.

Answer 1

Heya ! 

we know tanβ = B sinθ / A + B cosθ

Case 1 :

tan (90 + 37) = v(r) sin θ /7 + v(r) cos θ

- cot 37 = v(r) sin θ / 7 + v(r) cos θ

cot 37 = -v(r) sin θ / 7 = v(r) cos θ __________(1) 

Case 2 : 

tan (90 - 37 ) = v(r) sin θ / 25 + v(r) cos θ

cot 37 = v(r) sin θ / 25 + v(r) cos θ _________(2)

From (1) and (2) 

-v(r) sin θ / 7 + v(r) cos θ = v(r) sin θ / 25 + v(r) cos θ 

v(r)  cos θ = -16 _______________________(3)

Putting the value of (3) in (1) 

v(r) sin θ = 12 ________________________(4) 

from (3)²  + (4) ²

 [ v(r) ]² = 400    {sin ² θ + cos ² θ = 1 } 

v(r) = 20 m/s _________________________(5)

Putting the value of (5) into (3) 

cos θ = -4/5 

θ = 90 + 37 = 127 

v(r) = 20 m/s 

direction with vertical is 37°

Answer 2

Hope it helps

Thumbs up!