A straight highway leads to the …
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A straight highway leads to the foot of a tower a man standing at the top of the tower observes a car atan angle of depression of 30, which is approaching the foot of thetower with uniform speed 6 sec 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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Sia ? 6 years, 6 months ago
Let the speed of car be x m/sec.
{tex}\therefore {/tex} Distance covered in 6 sec. = 6 x.
{tex}\therefore {/tex} DC = 6x m
Let distance (remaining) CA covered in t sec
{tex}\therefore {/tex} CA = tx
Now in {tex}\triangle A D B{/tex} , AD = AC = CD = 6x + 9x
{tex}\therefore \quad \tan 30 ^ { \circ } = \frac { h } { 6 x + t x }{/tex}
{tex}\frac { h } { x } = \frac { 6 + t } { \sqrt { 3 } }{/tex} ....(i)
In {tex}\triangle{/tex}ABC
{tex}\frac{AB}{AC}=\frac{h}{tx}=tan60°=√3{/tex}
{tex}\frac{h}{x}=t√3….....(ii){/tex}
From (I)and(ii)
t√3(√3) = 6 + t
2t = 6 or t = 3 sec
Hence time taken by car from C to the tower is 3 sec.
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