Question

A man on the top of a vertical tower observes a car moving at a uniform speed. If it takes 8 minutes for the angle of depression to change from 30° to 60°, Find the time taken by car reach the tower?

solve by process ​

Answer 1

see the attachment for answers

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Answer 2

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Let the height of the tower be AD and the starting point of the car be at point B and after 6 seconds let the car be at point C. The angles of the depression of the car from the top A of the tower at point B and C are 30° and 60° respectively.

Distance travelled by the car from the starting point towards the tower in 6 seconds = BC

Distance travelled by the car after 6 seconds towards the tower = CD

We know that, speed = distance / time

The speed of the car is calculated using the distance BC and time = 6 seconds.

Using Speed and Distance CD, the time to reach foot can be calculated.

In ΔABD,

tan 30° = AD/BD

1/√3 = AD/BD

BD = AD√3 ....(1)

In ΔACD,

tan 60° = AD/CD

√3 = AD/CD

AD = CD√3 ....(2)

From equation (1) and (2)

BD = CD√3 × √3

BC + CD = 3CD [∵ BD = BC + CD]

BC = 2CD ....(3)

Distance travelled by the car from the starting point towards the tower in 6 seconds = BC

Speed of the car to cover distance BC in 6 seconds = Distance/Time

= BC/6

= 2CD/6 [from (3)]

= CD/3

Speed of the car = CD/3 m/s

Distance travelled by the car from point C, towards the tower = CD

Time to cover distance CD at the speed of CD/3 m/s

Time = Distance/speed

= CD / CD/3

= CD × 3 / CD

= 3

The time taken by the car to reach the foot of the tower from point C is 3 seconds.