- #1

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My approach:

[tex]y = -\frac{gt^2}{2} + v_0 cos( \alpha) t + h[/tex]

Projectile hits ground at:

[tex] t_{gnd} = \frac{v_0 sin( \alpha ) + \sqrt{ v_0^2 sin^2 ( \alpha) + 2gh}}{g}[/tex]

Now compute derivative of x and solve for alpha:

[tex]x_{max} = v_0 cos( \alpha) t_{gnd} [/tex]

[tex]\frac{dx_{max}}{d \alpha} = 0[/tex]

This last step where you solve for alpha is what buggers me. I get a huge quartic expression in alpha that does not simplify, I suspect the problem setter expects you to make some approximation but I can't figure it out.