Projectiles: Hitting x and y with initial height given.

[david_19]

Hi, we can determine the velocity to hit x and y point with angle of projection given. but can we do the same if the initial height of projection is given?

 

[zgozvrm]

I assume you mean that you know the target's horizontal and vertical distance away from the projectile's starting point, as well as the height of the projectile, but you do NOT know the projectile's initial velocity or angle of trajectory. Is that correct?

 

[K^2]

As long as you can ignore the drag, any problem of aiming a projectile can be reduced to a set of quadratic equations, so you can always find whatever missing information that you need.

 

[zgozvrm]

As long as you can ignore the drag, any problem of aiming a projectile can be reduced to a set of quadratic equations, so you can always find whatever missing information that you need.

That's not entirely true. You can find the missing information if your given enough information. Suppose I told you it took 5 seconds for a projectile to hit a target. That is not enough information to tell me it's initial velocity, angle of projection, or distance.

Or suppose I told you a target is 500 yards away. Can you tell me what angle I fired a projectile in order to hit it? No. You need more information like, say, the initial velocity. There are an infinite number of different velocities that I can fire a projectile and still hit my target, as long as I adjust the angle appropriately. Of course, there is a minimum velocity for any given distance.

 

[K^2]

Well, of course. You might as well point out that if you don't know anything about the problem, you don't know anything about the problem.

 

[zgozvrm]

Well, of course. You might as well point out that if you don't know anything about the problem, you don't know anything about the problem.

The point is that you can't necessarily find "whatever information you need" given any problem, which is what you said in your first post.

 

[K^2]

You can always find a closed-form expression. That's the important bit. The fact that the expression might have unknowns in it seemed obvious enough to not require further clarification.

So while I'll give you that my formulation may be fuzzy, I stand by my statement.

 

[zgozvrm]

The fact that the expression might have unknowns in it seemed obvious enough to not require further clarification.

While that may be obvious to some, it may not be obvious for all, which is why I pointed it out.

In the case of the OP, he is not even sure if you can quantitatively determine the angle of trajectory ("angle of projection," is actually what he said). By reading your post, he may think that it doesn't matter what's missing in a projectile-type problem, as long as you know something, you can figure out the rest.

Which, as I've pointed out more clearly, is NOT true.


Yes, you can write equations, for any projectile/trajectory problem without knowing any of the actual values, but that statement doesn't help the OP. You might as well have told him that apples grow on trees. It's a moot point.