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 30⁰ to 45⁰ , how long will the car take to reach the observation tower from this point?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Let speed of car be v. Then distance between change of angle will be 12v.

→ tan45° = h/vt

→ 1 = h/vt or h = vt

→ tan30° = h/(12v + vt)

By substituting values we get,

→ 1/√3 = vt/(12v + vt)

→ 12v + vt = √3vt

→ 12v = √3vt - vt

→ 12v = vt(√3 - 1)

→ 12v/(√3 - 1) = vt

On rationalizing we get,

→ 12v(√3 + 1)/2 = vt

→ 6(√3 + 1) = t

→ 6 × 1.73 + 6 = t

→ 16.38 minutes = t

Hence car will reach tower within 16.38 minutes.