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Q.

The maximum range of a shell fired from a gun is R=22.5 m. This gun is mounted on a platform that can move horizontally with a constant speed $υ = 15.0 m / s .$ At what angle in degree above the horizontal, must the gun be aimed to achieve maximum horizontal range? Neglect air resistance as well as height of the gun. Acceleration of free fall $g = 10.0 m / s^{2} .$

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answer is 60.

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Detailed Solution

$u = 15 m / s R = (\frac{2 u \sin θ}{g}) (15 + u \cos θ)$
$\frac{d R}{d θ} = 0 ∴ θ = 60^{0}$

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The maximum range of a shell fired from a gun is R=22.5 m. This gun is mounted on a platform that can move horizontally with a constant speed υ=15.0m/s. At what angle in degree above the horizontal, must the gun be aimed to achieve maximum horizontal range? Neglect air resistance as well as height of the gun. Acceleration of free fall g=10.0m/s2.