Projectile motion graph problems

[OhyesOhno]

Hi, I would like to ask about some questions relating to projectile motion. There are not necessarily many calculations involved. Anway, I am supposed to make a lab report concerning a projectile motion project. The project I did was launching tennis balls across the court using a lobster (machine that launches tennis balls like in movies). I alter the angles (independent variable) and see the displacement of the ball (dependent variable). I took 7 readings, 5 trials each.

Homework Statement

So my question is: what is the linear relationship between angle and distance? In my reports I am supposed to make a graph out of the data I obtained, and linearize the data I get and obtain an equation for that linear graph. The data I obtained, however is none like I've faced before. The data I got gives me a parabole-type of curve. I don't even know how to draw a line along the curve using Microsoft Excel for this kind of graph. I guess this is due to the fact that if you increase the angle, eventually the ball's displacement decreases.

Here's the data I obtained:

Angle (degrees) Average Displacement (m)
20.11 15.72
24.3 18.84
28.98 20.4
38.29 21.68
49.67 18.9
61.53 18.44
74.6 10.18

So how do I linearize the data? What is the relationship between the angle and displacement of a projected object?

Thanks and sorry if I post in the wrong section of the forum, I am new to the forum :)

 

[Kurdt]

Have you met the kinematic equations before? You can rearrange those to find a relationship between the angle and the distance and that should help you.

 

[merryjman]

Hmm, well when we see a graph that is not linear, that makes us angry. So we do stuff to our data set until we do get a linear relationship. Try messing with your angle data. For example, what if you find the tan() of each angle and graph those vs. displacement? Or sin()? Or cos()?

Something interesting in your data: it appears that the maximum displacement occurs somewhere between 30 and 50 degrees. What angle would make sense as being the best launch angle?