Question

A man on the top of a vertical observation tower observes a car moving at uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how long will the car take to reach the observation tower from this point?

Answer 1

Answer:

Step-by-step explanation:

PLZ CHECK THE ATTACHMENT

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LET SPEED BE X

LET TIME FROM B TO C BE Y

LET HEIGHT OF TOWER BE H

NOW

Distance from C to D = 12x

Distance from B to C = XY

Then

tan 30 = AB/BD

⇒ H/BC + BD = 1/√3

⇒H / XY + 12X = 1/√3

⇒H = (12+Y)X / √3                     ---------------(EQN 1)

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tan 45 = AB / BC

⇒ 1 = H / YX

⇒ H = YX                                               -----------------(EQN 2)

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FROM EQN1 AND EQN2

(12+Y)X / √3 = YX

⇒Y = (12+Y)/√3

⇒Y√3 = 12+Y

⇒Y(√3 - 1) = 12

⇒Y  = 12/ (√3-1)

NOW AS Y WAS TIME FROM B TO C

SO YOUR ANSER IS 12(√3-1) MINUTES

AND FOR TOTAL TIME IT IS

⇒12 + 12(√3-1)

⇒12(√3 + 1 - 1)

⇒12√3 MINUTES