Problem: A cannon that is capable of firing a shell at speed V is mounted on a vertical tower of height h that overlooks a level plain below.(adsbygoogle = window.adsbygoogle || []).push({});

(a) show that the elevation angle a at which the cannon must be set to achieve maximum range is given by the expression:

csc^2 a = 2*(1 + g*h/v^2)

I came up with the parabolic equations

x(t) = v*t*cos a

y(t)=0

z(t)= v*t*sin a - (1/2)*g*t^2 + h

I found the time that the projectile is in the air by setting z=0 and solving for t. Then I plugged that t into the equation for x to get the range so that

range= r = v*cos(a)*(v*sin a + sqrt( sin^2 a + 2*g*h/v^2 )

I then differentiated r with respect to the angle a and set the result equal to zero.

But here I am stuck. My procedure seems right to me but the algebra is gross and I can't seem to simplify it down to the form that they are asking for.

Thanks in advance for your help.

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# Homework Help: General case for pojectile motion from height h

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