Hello, our team has seen some of the very nice spreadsheets created for this season but we are in need of more than just a spreadsheet. We need an equation!
Has anyone derived an equation that just uses the initial velocity that the ball shoot out with.
We basically need an equation where all we know is V initial and we have to find the angle, final velocity, y final and x final.
We are looking for an equation with many variables obviously.
I feel like this would be a nightmare to figure out so that’s why I’m asking if anyone has already done it.
If you only have (know) V, and you dont know the angle, at least, or something that is based on the angle, you can’t have any equations.
An equation is a relationship between several variables; if you only have one variable, you can’t really make an equation.
As for finding the balls path when shot out with speed V and angle Theta, that’s easy, and has been done. For example, type into Wolfram Alpha, “projectile”, and it’ll take you to a nice projectile simulation screen that lets you calculate nifty scenarios and provides formulas to work with.
Velocity is a vector quantity, which means that it has both magnitude and direction. All you have is the speed, which is a scalar (and happens to be the magnitude of velocity, which is why they are often confused/used interchangeably by people who don’t know/forget the difference).
So, yes, you will need some sort of direction.
Now, you can use X=at^2+vt+x1, the position equation (and apply it to both X and Y), but this requires knowing starting position, the velocity component in the direction needed, and acceleration in that direction to find the position at any given time. And the velocity component requires knowing the angle…
In short, if you have both the horizontal and vertical components of velocity, or the magnitude and direction, you can solve this. Without either scenario, however, you’re going to be stuck for quite some time.
I was thinking that you have to at least know the angle and the x position but a team member is looking for an equation that is just variables. I don’t get how it would work – does this just not make sense.
like xf = xo +vxo t +1/2 at^2 is an equation with all variables but it can’t really tell us anything if we have just one variable
You’re right, it doesn’t make sense. It’s not a matter of difficulty of derivation; what you’re looking for is definitively indeterminate without more information*. An unfortunate fact of physics (and life).
You simply cannot determine a ball’s kinematic behavior based solely on its initial speed (scalar magnitude without angle). As an extreme example, take two balls shot at 5 m/s. One is launched at 45deg above the horizontal. The other is launched straight down. Which has a larger x displacement?
*Cue someone telling me this is too sweeping a generalization. do’h