question_answer

A person is standing on a tower of height \[15(\sqrt{3}+1)\,m\] and observing a car coming towards the tower. He observed that angle of depression changes from\[{{30}^{o}}\]to\[{{45}^{o}}\]in 3 sec. What is the speed of the car [Karnataka CET 1998]

A) 36 km/hr

B) 72 km/hr

C) 18 km/hr

D) 30 km/hr

Correct Answer: A

Solution :

\[CD=h\text{ }(\cot {{30}^{o}}-\cot {{45}^{o}})\] \[15\,(\sqrt{3}+1)\,[\cot {{30}^{o}}-\cot {{45}^{o}}]\] \[=15\,(\sqrt{3}+1)\,(\sqrt{3}-1)\] = \[15\,(3-1)=30m\] Speed = \[\frac{30}{1000}\times \frac{60\times 60}{3}km/hr\]= \[36km/hr\].