Question

Angle of depression from tower top to A is 30°. After 20 seconds at B, it is 45°. Time taken from B to reach the base is :

• A. 10
• B. 10(√3 + 1)
• C. 10√3
• D. 10(√3 - 1)

Hint:

In problems of uniform speed, time taken is proportional to distance: $T_1/D_1 = T_2/D_2$.

Answer 1

The Correct Option is B

Step 1: Let tower height be $h$. Distance to base from A = $h\cot 30^\circ = h\sqrt{3}$.
Step 2: Distance to base from B = $h\cot 45^\circ = h$.
Step 3: Distance AB = $h(\sqrt{3}-1)$. Time for AB = 20s.
Step 4: Speed $v = \frac{h(\sqrt{3}-1)}{20}$. Time for B to base = $\frac{h}{v} = \frac{20}{\sqrt{3}-1}$.
Step 5: Rationalize: $\frac{20(\sqrt{3}+1)}{2} = 10(\sqrt{3}+1)$.