2.1: Ball Toss Project

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Purpose of the project: get familiar with the idea of creating a velocity function based on position data

$Shows several still images of a ball being tossed with the following heights: 20cm, 40cm, 55cm, 63cm, 67cm$

Above are frames from a video of a simple ball toss. Every other frame from the 30 frames per second video is shown, so the time between the frames is approximately $quicklatex.com-e87fc9a2e559c3d2773c6c3742090142_l3.png$ of a second.

Fill in the position data for each time in the table below. Velocity is usually defined as $\frac{\text{Position}}{\text{Time}}$. How could you calculate velocities for each data point? Fill these in as well.

Time (s)	Position (cm)	Velocity (cm/s)
$0$
$\frac{1}{15}$
$\frac{2}{15}$
$\frac{3}{15}$
$\frac{4}{15}$

Create two graphs, either by hand or with graphing software: position versus time, and velocity versus time. In each case, time is the $x$-axis, while the $y$-axis is position in the first graph and velocity in the second graph. How are the two graphs related?
Going from a position graph to a velocity graph like this is called a derivative, which we’ll talk a lot more about in upcoming chapters.
While your velocity graph is probably not a perfect line, imagine that it is linear for a second. What is the slope of the velocity graph? This is the rate of acceleration due to gravity, an important quantity in physics.

Time (s)	Position (cm)	Velocity (cm/s)
\(0\)
\(\frac{1}{15}\)
\(\frac{2}{15}\)
\(\frac{3}{15}\)
\(\frac{4}{15}\)

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