Calculating Minimum Required Velocity

[ByronT]

This is a tough question. I'd like to know if anybody can find a good solution. It isn't required for any of my classes, but I'd like to see a theoretical result. It seems like it should be a simple projectile motion problem, but it's not that easy.

Let's say there's a building x₁ meters away and y₁ meters tall. So, we only know x and y. What is the minimum initial velocity at which a projectile can be launched to "land" on top of this building? Assume that the projectile is launched from the origin.

Obviously, we know the standard projectile equations. We know the x-distance and y-distance we must travel. We know how to convert v_initial to v_x and v_y. But how do we find the minimum v_initial and its corresponding theta?

Any help would be appreciated.

 

[w3390]

So you want the projectile to be able to stop on top of the building, not just clear it?

 

[ByronT]

I figured it out. Found something on Wikipedia. I'll let other people look at it for a day before I post what I found.