A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man\’s eye when at a distance of 60 meters from the tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?
(A)
32 kmph
(B)
36 kmph
(C)
40 kmph
(D)
44 kmph
Answer: (A)
Explanation:
Let the tower be PQ and the boat be at positions R and S when making angles of 45° and 30° respectively.
Given, PR = 60 m. Now, PQ/PR = tan 45° = 1. So, PQ = PR = 60 m.
Again, PQ/PS = tan 30° = 1/√3. So, PS = 60 * √3 m = 103.92 m.
Distance covered in 5 seconds = 103.92 – 60 = 43.92 m. Speed in kmph = (43.92/5) * (18/5) = 32 kmph (approximately)
Quiz of this Question
Please comment below if you find anything wrong in the above post