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.