A man at the top of a tower watches a car coming straight towards the tower at a steady speed. The angle of depression of the car changes from 45° to 60° in 10 minutes. How much longer will the car take to reach the tower?

Question

Accepted Answer

5(√3 + 1) minutes. With tower height h, the distances are h and h/√3. In 10 min the car covers h(1 − 1/√3); the remaining h/√3 takes 10 × (1/√3)/(1 − 1/√3) = 10/(√3 − 1) = 5(√3 + 1) minutes ≈ 13.7 min.

A man at the top of a tower watches a car coming straight towards the tower at a steady speed. The angle of depression of the car changes from 45° to 60° in 10 minutes. How much longer will the car take to reach the tower?

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