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प्रश्न
A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km/h. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target?
उत्तर
The velocity of the fighter plane at a height h = 1.5 km = 1500 m is given as u = 720 km/h = `720 * 5/18` = 200 m/s
Let the plane drops the bomb t seconds before the target is exactly below the plane.
Then in t seconds, the bomb must cover the vertical distance of 1500 m under free fall with an initial velocity of zero.
Hence, h = `ut + 1/2 gt^2`
That gives, `1500 = 0 + 1/2 10t^2`
`t = sqrt(300) = 10sqrt(3) s`
Now distance covered by the plane is `ut = 200 xx 10sqrt(3) = 2000sqrt(3)`
Hence, `tan theta = 1500/(2000sqrt(3)) = sqrt(3)/4`
Therefore, `θ = tan^-1 sqrt(3)/4` = 23°42'
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