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**Deriving a Launch Angle Equation -- Projectile Motion -- Please Help**

This is physics in the area of projectile motion. My class and I are doing a lab where we have to calculate the launch angle in order to perform a successful lab. The experiment is as follows: the projectile launcher releases a bullet and the goal is to hit the moving target as it falls down (via gravity). In the diagram I provided (in the 2nd attached file), the three circles is the target which in real life will be a thick piece of cardboard.

Now, prior to conducting the lab, we have to derive a launch angle equation. That is, θ = ?

*something*...

We can use the 5 kinematics equations. However, as I've written in the attached files, the equation can only consist (but not necessarily all) of dx (range), dy, and h. Vi, Vf, or ∆t cannot be used (acceleration [9.8] can be used).

As apparent in the first attached file, I have attempted to get to an equation. I started with thinking that, in order for the bullet to hit the target, the vertical distance (dy) of the bullet has to be the same as h-x (where the target will be). Therefore dy= h - x. And ∆dt (distance of target) is what I put for h-x. Hopefully the rest is clear enough to be comprehendable.

I am

__not at all__sure if what I've done is correct. If it is, I'm not quite sure what to do next.

So any help or hints would be greatly, greatly appreciated.

Thanks in advance

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