A person on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 6 minutes for the angle of depression to change from 30^{\circ} to 45^{\circ}, and further t minutes to reach the tower, which one of the following is correct?
- A. 7.7 \lt t \lt 8
- B. 8 \lt t \lt 8.3 ✓
- C. 8.3 \lt t \lt 8.6
- D. 8.6 \lt t \lt 8.9
Correct Answer: B. 8 \lt t \lt 8.3
Explanation
Let tower height be h. The distance at 30^{\circ} is h\sqrt{3} and at 45^{\circ} is h. The distance covered in 6 min is h(\sqrt{3}-1). To cover the remaining distance h, time t = \frac{6}{\sqrt{3}-1} = 3(\sqrt{3}+1) \approx 3(2.732) = 8.196 min. Hence, 8 \lt t \lt 8.3.
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