Position with respect to velocity

[Robb]

Homework Statement

A cannon with muzzle speed of 1000m/s is used to start an avalanche on a mountain slope. The target is 2000m horizontally from the cannon and 800m above the cannon. At what angle above the horizontal should the cannon be fired.

Homework Equations

The Attempt at a Solution

I look at this as tan(x)=8/20 but, this doesn't account for the fact that the projectile will have a curve to it's trajectory. I'm not sure how to link that curve to the position it will land in order to get the angle.

 

[RUber]

You can first find the time it will take to impact the target in terms of elevation angle, then solve the problem substituting that in for time.

It should look like:
$t_f = 2000m/(1000*cos(\theta) m/sec)$
$y(t_f)=800 = 1000*sin(\theta)t_f - 4.9 t_f^2$