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Math Help - Projectiles question

  1. #1
    Junior Member silvercats's Avatar
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    Projectiles question

    Gun in a fortress can can shoot missiles from a velocity of √(2gk).Gun is situated "h" meters high from the sea level.How to show that maximum horizontal range of a missile sent by the gun is 2√[k(k+h)] ?

    I did this ,but not even close to the 2√[k(k+h)]

    x=√(2gk)cos Θ*t

    flying time : 0=√(2gk)Sin Θ*t - (g/2)tē
    t=2 Sin Θ/g

    x=√(2gk)cos Θ*2 Sin Θ/g
    For the maximum range Θ has to be 45degrees

    therefor
    x=√(2gk)(1/√2)*2 (1/√2)/g
    x=√(2gk)/g <<<so that has to be the Horizontal distance.What else.......
    how am i supposed to get 2√[k(k+h)]
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  2. #2
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    Quote Originally Posted by silvercats View Post
    Gun in a fortress can can shoot missiles from a velocity of √(2gk).Gun is situated "h" meters high from the sea level.How to show that maximum horizontal range of a missile sent by the gun is 2√[k(k+h)] ?

    I did this ,but not even close to the 2√[k(k+h)]

    x=√(2gk)cos Θ*t

    correction ...

    flying time : 0 = h + √(2gk)Sin Θ*t - (g/2)tē
    also ... max range of a projectile launched from a height h at an angle \theta will not be 45^\circ

    \theta_{max} = \arctan\left(\frac{v_0}{\sqrt{v_0^2 + 2gh}}\right)
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