Question

A straight highway leads to the foot of a tower. Ramaiah standing at the top of the tower observes a car at an angle of depression 30°. The car is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.​

Answer 1

Answer:

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Answer 2

QUESTION :-

A straight highway leads to the foot of a tower. Ramaiah standing at the top of the tower observes a car at an angle of depression 30°. The car is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

SOLUTION :-

⭐ Refer the given attachment ⭐

• Let the distance travelled by the car in 6 seconds = AB = x meters.

• Height of the tower CD = h meters

• Remaining distance to be travelled by the car BC = d mts & AC = AB + BC = (x + d) meters

∠PDA = ∠DAC = 30°

∠PDB = ∠DBC = 60°

From ∆BCD

=> tan30° = CD/AC

=> √3 = h/d

=> h = √3d ________ equation ( 1 )

From ∆ACD

=> tan30° = CD/AC

=> 1/√3 = h/(x + d)

=> h = (x + d)/√3 ________ equation ( 2 )

From equation ( 1 ) & ( 2 ), we have

=> x + d/√3 = √3d

=> x + d = 3d

=> x = 2d

=> d = x/2

Time taken to travel 'x' meters = 6 seconds

Time taken to travel the distance of 'd' meters

i.e., x/2 meters = 3 seconds.