Graphical and Mathematical Representation


Find the graphical and mathematical representation of an object shot from a slingshot.


See attached paper for apparatus.

Method/Procedure Summary:

- Gather a slingshot, ball, tape, measure tool, table, scale, stopwatch, protractor on a table
- Keep the slingshot from moving around on the table by applying tape
- Put the ball on the slingshot and measure the distance it is pulled back and keep the - distance consistent
- Measure the weight of ball in kilometers
- Measure the angle of the launch (independent)
- Launch the ball using the slingshot while measuring the time in seconds (dependent)
- Measure how far the ball traveled horizontally in meters(dependent)
- Repeat steps 5-7 for 6 trials


pull length: 0.05 (m)
ball: 0.0023 (kg)

angle (?) horiz dis (m) time (s) horiz vel (m/s)
5 0.46 0.21 2.19
10 0.83 0.39 2.13
20 1.41 0.69 2.04
30 1.80 0.88 2.05
40 1.98 0.98 2.02
45 2.00 0.99 2.02
90 0.00 1.02 0.00

horiz vel (m/s) = horiz dis (m) / time (s)


See attached paper for graphs, motion maps, interaction schemes, force diagram.

The horizontal and vertical velocities and displacement are independent of each other. To reach a maximum vertical displacement, a 90? angle of launch must be used. To reach a maximum horizontal displacement, a 45? angle of launch must be used. To reach a maximum time of flight, a 45? and 90? angle of launch must be used.

Horizontal displacement vs. initial horizontal velocity

The y-intercept is initial velocity of the ball. The slope is acceleration of the ball.

Equation: Velocity (m/s) = 0.06 (s ^2) Dis (m) ^2 ? 0.26 (s) Dis (m) + 2.30 Vel (m/s)

Initial vertical velocity vs. time of flight


The experiment was interesting, but very confusing. We were unable to calculate the initial vertical velocity of the ball at a 90? angle of launch. Because of this one of graphs, along with its supplement data were not calculated. But we still learned many things about projectiles from this project. We learned that the horizontal and vertical displacement and velocities are independent of each other. We also learned that 45? angle of launch will give you a maximum horizontal displacement and 90? angle of launch will give you a maximum vertical displacement. We learned that doing the experiment on the grass lawn was much better than on cement because the grass stopped the movement of the ball. The project can be improved by review of what will be done before that starting of the project. Also a more open project allowing us to vary the project would also improve the experiment.