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An observer on the top of a tree ,finds ...

An observer on the top of a tree ,finds the angle of depression of a car moving towards the tree to be `30^@` .After 3 minutes this angle becomes `60 ^@`.After how much more time , the car will reach the tree ?

Text Solution

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Let the observer be at point A. Also let D be intitial position of the car and C the position after 3 minuts .

In `Delta ABD, BD = h cot 30^@`
`In Delta ABC , BC = h cot 60 ^@`
`therefore CD = BD - BC `
`rArr d=h cot 30 ^@ - h cot 60 ^@`
`therefore " speed of the car "= (h(cot 30 ^@- cot 60 ^@ )/(3)`
`therefore` Time required to travel distance BC
`= (h cot 60 ^@ xx 3)/(h(cot 30 ^@ - cot 60 ^@)`= 1.5 minute
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