1. ## 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)]

2. Originally Posted by silvercats
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 $45^\circ$

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