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An aeroplane is flying at a constant hei...

An aeroplane is flying at a constant height of 1960 m with speed `600 kmh^(-1)` above the ground towards point directly over a person struggling in flood water. At what angle of sight with the vertical should be pilot release a survival kit if it is to reach the person in water ? `(g = 9.8 ms^(-2))`

A

`45^(@)`

B

`30^(@)`

C

`60^(@)`

D

`90^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Plane is flying at a speed `= 600 xx (5)/(18) = (500)/(3) ms^(-1)` horizontally (at a height 1960 m)

Time taken by the kit to reach the ground
`t = sqrt((2h)/(g)) = sqrt((2 xx 1960)/(9.8)) = 20s`
in this time the kit will move horizontally by
`x = ut = (500)/(3) xx 20 = (1000)/(3)m`
So tha angle of sight
`tan theta = (x)/(h) = (1000)/(3 xx 1960) = (10)/(5.88) = 1.7 = sqrt(3)` or `theta = 60^(@)`
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