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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Answer 1

Answer:

3 sec

Explanation:

here distance cover in 6 sec is

$\frac{h}{tan30} - \frac{h}{tan60} = distance \: in \: 6 \: second$

which gives

$distance = \frac{2h}{ \sqrt{3} }$

now according to distance =velocity x time

we can find the velocity with given time 6 sec

that is

v=

$\frac{h}{3 \sqrt{3} } = velocity$

now time taken to cover the remaining distance d=h/tan60 with above velocity is

$\frac{h}{ \sqrt{3} } = \frac{h}{3 \sqrt{3} } \times t$

t= 3 sec