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 an uniform speed . Six second 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

Let the distance traveled by the car in 6seconds=AB=X metres

Height of the tower CD=h metres

The remaining distance to be traveled by the car BC =d metres

AC =AB+BC=x+d metres

ANGLE PDA=ANGLE DAC=30

ANGLE PDB=ANGLE DB*C=60

TRIANGLE BCD TAN60=CD/BC=root3=h/d

h=root3d

TRIANGLE ACD TAN30=CD/AC

1/root3=h/(x+d)

h=(x+d)/root3

(x+d)/root3=root3d

x+d=3d

x=2d

d=x/2

Time taken to travel x metres =6seconds

Time taken to travel the distance of D metres i. e., x/2=6/2=3seconds



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Answer 2

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