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Question

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which 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.


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Solution

Step 1: Draw the diagram according to the question.

Let AB be the tower. D is the initial andC is the final position of the car respectively.

As man is standing at the top of the tower so, Angles of depression are measured from A.

BC is the distance from the foot of the tower to the car.

Step 2: Find relation between BC and CD.

From

ΔABC,tan60°=ABBC

3=ABBCBC=AB3AB=3BC

Again in ABD

tan30°=ABBD13=ABBDAB=BD3

Now, comparing Height AB, we get

3BC=BD3 (Since LHS are same, so RHS are also same)

3BC=BD3BC=BC+CD2BC=CDorBC=CD2

Here, distance of BC is half of CD.

Step 3: Find the required time.

Hence, the time taken is also half.

Since, Time taken by car to travel distance CD=6sec.

So, Time taken by car to travel BC=62=3sec.


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