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A plane is flying along a road with a co...

A plane is flying along a road with a constant speed of 600 km/h towards a point on the road. Its angle of elevation changes from `30^(@)" to "60^(@)` in 12 seconds. Find the vertical height of the plane.

Text Solution

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Let 'O' be a fixedpoint on the road and the plane is flying towards O. Now A and B are two positions of the plane.
Let the height of plane
`AP=BQ=h`
Given that, `angleAOP30^(@)" and "angleBOQ=60^(@)`
Now, AB=distance corved by plane in 12 sec
`=(600xx5/18)xx12=2000m`
Let OQ = x
In `DeltaBOQ`,
`tan30^(@)=h/xrArrsqrt3=h/x`
`rArr x=h/sqrt3`
In `DeltaAOP`,
`tan30^(@)=(AP)/(OP)rArr1/sqrt3=h/(x+2000)`
`rArr hsqrt3=x+2000`
`rArr hsqrt3=h/sqrt3+2000" [from(1)]`
`3h=h+2000sqrt3`
`rArr 2h=2000xx1.732=3464 mrArr h=1732 m`
Therefore the vertical height of plane = 1732 m
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