How Can Graphs Help Analyze Muzzle and Impact Velocity Data?

[Azndoode1]

Homework Statement

For a lab in Physics C, we're supposed to find the muzzle and impact velocity of a dart gun. We found x-distance, y-distance, and angle fired at, however, we were not allowed time. Our teacher wants us to graph data that is important, but I don't see how a graph would be able to show anything here...

Homework Equations

The Kinematics equations.

The Attempt at a Solution

I derived the equation for Initial Velocity to be ∆x/(√((2∆y-2∆x tan⁡(θ))/g) cos⁡(θ)). However, I'm at a loss as to what my graphs could possibly show.

 

[NascentOxygen]

Its motion vertically is determined by g and its initial vertical velocity component. Its motion horizontally is determined by its initial horizontal velocity component. You may not have measured its time of flight, but you do know that the time it takes to travel that horizontal distance is exactly equal to the time it took to perform its vertical motion.

I presume you are considering the effects of air resistance to be negligible? Otherwise, the picture is starting to get complicated.

 

[Azndoode1]

You presume correctly.

I'm not quite sure I understand what you're saying about it's motion vertically / horizontally?

 

[NascentOxygen]

The motion near the Earth's surface of anything in 2 dimensions can be considered as being a combination of 2 separate and independent movements: vertical and horizontal. The net result is the sum of these. Horizontal motion is not affected by gravity, since gravity acts vertically downwards.