Question

A man at top of a vertical observation tower observes a car moving at uniform speed coming directly towards the tower. If it takes 16 minutes for angle of depression to change from 30degree to 45 degree, how much after this will the car reach the observation tower?

Answer 1

$\huge{\boxed{\mathtt{\red{ANSWER}}}}$

in ∆ABD,

tan 30° = 1/√3 = AB/BD

BC+CD/√3 = AB ----------(1)

in ∆ ABC,

tan 45° = 1 = AB/BC

AB = BC ----------------(2)

from both eqn , we get,

AB(√3-1) = CD ----------(3)

Now, let speed of car = X m/min

so, CD = 16x ( D = S*T) -------(4)

using (3) & (4) we get, now,

X = AB(√3-1)/16 ---------(5)

now, car has to cover BC distance ,

Time car will take = 16BC/AB(√3-1)

since AB = BC

Time = 16/(√3-1) = 21.9 min (Ans)

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