Question

An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be 30^∘. After 3 minutes this angle becomes 60^∘. After how much more time will the car reach the tree?

• A. 4 min.
• B. 4.5 min.
• C. 1.5 min.
• D. 2 min.

Hint:

In angle of elevation/depression problems, use tanθ=fracheightdistance.

Answer 1

The Correct Option is C

Step 1: Let the height of the tree be h. Initial distance: x = (h)/(tan 30^∘) = √(3)h After 3 minutes: y = (h)/(tan 60^∘) = frach√(3) Step 2: Distance covered in 3 minutes: √(3)h - frach√(3) = \frac2h√(3) Step 3: Speed: v = \frac2h3√(3) Step 4: Remaining distance: frach√(3) Step 5: Time required: t = frach/√(3)2h/(3√(3)) = (3)/(2) = 1.5 min