# Projectiles using calculus

• Aug 25th 2010, 05:43 AM
differentiate
Projectiles using calculus
Show that to hit a target h metres above what was its maximum range position on
a horizontal plane, the initial speed of a projectile projected at the same angle as before, must be increased from V to $\frac{V^2}{\sqrt[]{V^2 - gh}}$ m/s (air resistance is neglected.)

Thanks

I had the equations of motion as
x = $Vtcos\Theta$
and
y = $\frac{-gt^2}{2} + Vtsin\Theta$

Putting y = 0
t = 0 or $t = \frac{2Vsin\Theta}{g}$
thus max range is $x = \frac{2V^2sin\Thetacos\Theta}{g}$

new projectile must hit $( \frac{2V^2sin\Thetacos\Theta}{g}, h)$

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what shall I do next?

I gather that my new speed must have theta in it. however, the question does not have a theta. There is nothing I can do that eliminates the theta. Is the question wrong?