We have a mini catapult that fires balls at a velocity of 5 m/s. It is placed 1 meter above the ground and pointed at an angle towards the positive x-axis. What angle(s) do we need to set it to in order to hit a target on the ground at x=2.7 meters?

In other words:

(assuming the catapult is standing in the origin)

My thinking so far

First express the velocity in thex-direction andy-direction separately:

Then find a way to expresstin terms of the angle and the positions:

Use what I now have to writeyas a function of theta:

Since I know x, y and v, I should now be able to solve for theta.

Have I set this up correctly? Is there maybe an easier way to calculate the angle? And finally, if this is the best way to find it, how the hell do I solve for theta??