Projectile Motion: Finding angles given velocity and impact coordinates

[joepeezy]

I'm not looking for someone to work this one out for me, and I know I have done this type of problem in entry level physics, but it's popped up again in dynamics, and physics is mostly a blur these days.

Given the muzzle velocity and impact coordinates of a rifle, find the angles of elevation that will make the shot.

we can derive two equations with two unknowns, t and θ, however I can't remember the trick to solving this equation.

I can get the answer with my favorite calculator, but that's cheating, and I want to be able to do this one in a pinch.

Any hints you guys can provide would be wonderful,

Joe

 

[Delphi51]

There are three equations. One for the horizontal motion at constant speed, and for the vertical motion - one for distance and one for velocity. Usually you choose one horizontal equation and one vertical one, eliminate time and solve for velocity.