CBSE Class 10 Answered

Increase in the angle of depression means the car is moving towards the building.

Let X be the initial distance of car from building.

(1)         tan 30 = H/X                       .... H, being the height of the building.

V, the speed of the building, then in the  6 min, car travels 6V.

(2)         tan 60 = H/(X - 6V)

When the car reaches the building, angle of depression will be 90°.

And we have to find the time taken to reach the building, X/V = T.

Dividing (2) by (1),

tan 60 /tan 30 = X/(X - 6V)

3 = (X/V)/(X/V - 6)

3 = T/(T-6)

3T - 18 = T

T = 9 min.

The car will take 9 min to reach the building from it's initial position.

Regards,

Team,

TopperLearning.