When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1+β) v, this angle changes to 45°. The value of β is close to :

Question

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1+β) v, this angle changes to 45°. The value of β is close to : (A) 0.41 (B) 0.50 (C) 0.37 (D) 0.73

Tardigrade Admin · Accepted Answer

Rain is falling vertically downwards vec v r / m = vec v r - vec v m

tan 60°=( v r / v m )=√3 v r = v m √3= v √3 Now, v m =(1+ B ) v and θ=45°

tan 45=( v r / v m )=1 v r = v m v √3=(1+β) v √3=1+β ⇒ β=√3-1 =0.73

$0.41$

$0.50$

$0.37$

$0.73$

0.41

0.50

0.37

0.73

Rain is falling vertically downwards vr/m​=vr​−vm​ tan60∘=vm​vr​​=3​ vr​=vm​3​=v3​ Now, vm​=(1+B)v and θ=45∘ tan45=vm​vr​​=1 vr​=vm​ v3​=(1+β)v 3​=1+β ⇒β=3​−1 =0.73

$0.41$

$0.50$

$0.37$

$0.73$