question_answer

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

A) 4 min.

B) 4.5 min.

C) 1.5 min.

D) 2 min.

Correct Answer: C

Solution :

\[d=h\cot {{30}^{o}}-h\cot {{60}^{o}}\text{ and time }=\]3 min. \[\therefore \]  Speed = \[\frac{h(\cot {{30}^{o}}-\cot {{60}^{o}})}{3}\] per minute It will travel distance \[h\cot {{60}^{o}}\] in \[\frac{h\cot {{60}^{o}}\times 3}{h(\cot {{30}^{o}}-\cot {{60}^{o}})}\] = 1.5 minute.