The question is from Physics, but all I need is help on solving maths. So basically, i am trying to find out the optimal angle for projectile motion from a certain height and I end up with these two equations:

$$0=h + R \tan \theta - R^2 \frac g{2u^2}(1 + \tan^2 \theta) \tag1$$

$$R= \frac{g}{u^2}cot \theta \tag2$$ where, h = height of the tower

R= maximum distance travelled by the stone (Range)

g=gravitational constant

$\theta$ = angle of the projection

Can anyone help with how do I solve this two equations to obtain this:

$$\theta = \arctan \left(\frac u{\sqrt{u^2+2gh}} \right)$$

Thanks. :)

P.S.: I did tried to solve by substituting R in equation (1), but my final answer way very long and very complicated.

  • $\begingroup$ Just replace all occurencies of $R$ in the first equation using the second equation, then solve the quadractic equation with respect to $\tan ^2\theta$. $\endgroup$ – TZakrevskiy Dec 15 '14 at 19:11
  • $\begingroup$ @TZakrevskiy I did it the same way.. but it was way too complicated.. $\endgroup$ – aavatar Dec 15 '14 at 19:12
  • $\begingroup$ Look at math.stackexchange.com/questions/571/… $\endgroup$ – Ross Millikan Dec 15 '14 at 19:13
  • $\begingroup$ my result is also not yours, are you sure that you have made no typo? $\endgroup$ – Dr. Sonnhard Graubner Dec 15 '14 at 19:35
  • $\begingroup$ @Dr.SonnhardGraubner I pretty much sure... there is not typo $\endgroup$ – rndflas Dec 15 '14 at 19:43

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