Question

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly toeqrds it.If takes 12 min for the anagle of depresion to change from 30 degree to 45 degree

Answer 1

Answer:

16.39 mins

Step-by-step explanation:

Let say Height of tower = H

D₁ - Initial Distance from tower

D₂ - Distance from tower after 12 Mins

Tan 30  = H / D₁

=> 1/√3  = H/ D₁

=> D₁ = H√3

Tan 45  = H / D₂

=> 1  = H/ D₂

=> D₂= H

Distance Covered in 12 Mins = H√3 - H = H(√3 - 1)

Distance Remained to cover = H

H(√3 - 1)  covered in  12 mins

1  covered in  12/H(√3 - 1)   mins

H covered in  12H/H(√3 - 1)   mins

= 12/(√3 - 1)

= 6(√3+ 1)  minutes

= 16.39 mins

in 16.39 mins , it will reach tower