Question

A man on the top of a vertical observation tower observes a car moving at a 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:

16.39 minutes (or) ~983 seconds

Step-by-step explanation:

Let the tower be AB and the positions of the car be C and D.

Let height of tower = AB = h and CD = x and AC = y.

Given, ∠ACB = 45° and ∠ADB = 30°

(i)

⇒ AB/AC = tan 45°

⇒ h/y = 1

⇒ h = y.

(ii)

⇒ AB/AD = tan 30°

⇒ h/CD + AC = 1/√3

⇒ h/x + y = 1/√3

⇒ x + y = √3 h

⇒ x + h = √3 * h

⇒ x = h(√3 - 1).

Now, h(√3 - 1) is covered in 12 minutes.

So, h will be covered in [12/h(√3 - 1)] * h

⇒ 12/(√3 - 1) min

⇒ [12/√3 - 1] * [√3 + 1/√3 + 1]

⇒ 12(√3 + 12)/3 - 1

⇒ 6√3 + 6

⇒ 6(1.732) + 6

⇒ 16.3 minutes

Hope it helps!

Answer 2

Step-by-step explanation:

the answer is explained below