I am trying to find the optimal angle for a projectile to travel a maximum horizontal distance.

I've been given the projection has mass $1kg$ and initial velocity $150m/s$. The equation for air resistance I'm using is $$ F_{air} = - k|v|^2 $$

where $k = 0.001$

I'm currently trying to use the following equation to find the horizontal distance:

$$ \int v_x dt = \int\frac{1}{\frac{1}{v_o\cos(\theta)} + \frac{kt}{m}} dt $$

but I'm unsure what values to integrate between on the right integral as I do not know the time it will take the projectile to land.

Please can someone give me a hint on what I should do next.

  • 1
    $\begingroup$ If the ground is flat, you need to solve for $y(t)=0$. $\endgroup$ – Yves Daoust Apr 20 '16 at 9:11
  • $\begingroup$ @YvesDaoust Yes, the ground is flat. Thank you $\endgroup$ – Nique Apr 20 '16 at 9:12
  • $\begingroup$ @YvesDaoust So $\int v_x dt = 0$ and then rearrange to find $\theta$? $\endgroup$ – Nique Apr 20 '16 at 9:19
  • $\begingroup$ No. $\int v_y\,dt=0$ ! $\endgroup$ – Yves Daoust Apr 20 '16 at 9:21
  • $\begingroup$ @YvesDaoust But I have no equations involving $v_y$?? $\endgroup$ – Nique Apr 20 '16 at 10:57

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