A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A , with uniform speed. At that point, angle of depression of the boat with the man's eye is 30 ° (Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B , where the angle of depression is 45 ° . Then the time taken (in seconds) by the boat from B to reach the base of the tower is :

Question

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A , with uniform speed. At that point, angle of depression of the boat with the man's eye is 30 ° (Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B , where the angle of depression is 45 ° . Then the time taken (in seconds) by the boat from B to reach the base of the tower is :, 10, 10 ( 3 - 1 ), 10 3, 10 ( 3 + 1 )

MARKS App · Accepted Answer

Let speed of boat is u m / s and height of tower is h meter & distance A B = x metre ∴ x = hcot 30 ° - hcot 45 ° ⇒ x = h ( 3 - 1 ) ∴ u = x 20 = h ( 3 - 1 ) 20 m / s ∴ Time taken to travel from B to C (Distance = h meter) = h u = h h ( 3 - 1 ) 20 = 20 3 - 1 = 10 ( 3 + 1 ) sec .

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