Question

B 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.​

Answer 1

Answer:

3 seconds

Step-by-step explanation:

Let the distance of CD be 'x' meter.

Speed= Distance/Time

=x/6 m/s.

Since the speed is uniform throughout the journey, the same speed will be used to cover BD as well......(1)

Let the tower AB have a height of 'h' meter.

Now, tan60=h/BD

tan60=√3

This implies that h/BD=√3

Which means that BD=h/√3........(2)

tan30=h/BC

tan30=1/√3

This implies that h/BC=1/√3

Which means that BC=h√3..........(3)

BC-BD=x ( According to the figure)

This implies that

h√3-h/√3=x (substituting the values of BC and BD from (2) and (3)).

This implies

(3h-h)/√3= 2h/√3=x

This implies that h= x√3/2........(4)

Now, BD=h/√3 (from(2))

Substituting the value of h from (4), we get that:

BD= (x√3/2)÷2=x/2............(5)

Now, Speed= Distance/time.

We found the distance of BD to be x/2 from equation (5). And Speed will be x/6 from equation (1)

This implies that

x/6=(x/2)÷time taken

This implies that time taken is (x/2)÷(x/6)= 3 seconds.

Hence, the time taken to cover that Distance is 3 seconds

(Ans.)

Answer 2

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