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)0.50
(B)0.41
(C)0.37
(D)0.73✓ Correct
Answer: (D)
Solution
At speed v the rain appears to come in at 60∘ to the horizontal, so tan60∘=vVr and the rain's fall speed is Vr=3v. At the higher speed (1+β)v the apparent angle is 45∘, so tan45∘=(1+β)vVr, giving Vr=(1+β)v. Equating the two expressions for Vr, 3v=(1+β)v, so β=3−1≈0.73.
JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option
