Motion of a Falling Object

Tracking a falling ball

Purpose: Use Calculus to examine the motion of a falling object.

Equipment needed:

ball (smaller, heavier, is best to lower air resistance); cell phone or digital camera;

person not afraid of heights

Gathering experimental data

Take a movie of a falling ball with your cellphone, digital camera, or other device. ball drop.gif

Using a video editor such as Windows Movie Maker (included in Windows), iMovie, or one on your cellphone, find the position vs. time of the ball.

You will need the timer on the movie editor to find the time at each position of the ball:

Using your initial height (position), s₀ meters or feet, at t₀ = 0 sec
Whatever your timer reads the instant the ball is dropped top becomes 0 sec.
Measure from the floor to the center of the ball in your movie.
You need to scale this to meters or feet using a ratio.

Example:
You drop the ball from 5 m high and your ruler measures 20 cm from the ground to the highest position in the movie.
Let's say after a certain time, the distance from the ground to the middle of you ball in the movie is 4 cm.
Then 4cm/20cm = (actual height)/5m That is, the movie ratio = the actual ratio.

Data Table:

time (sec)	position (height) (m or ft)
t₀ = 0	s₀ = m or ft

Time to hit the ground from your video sec

Plot these data on your calculator or computer and do a quadratic regression to find the parabola of best fit.
(TI Calculator Stat | Edit Stat | Calc )*

You can also use a spreadsheet such as Excel if that's on your laptop.
You will need to put the data in 2 columns and create a chart (Insert | Scatter Plot)
Then right click on any data point and Insert | Trendline | Polynomial | Degree 2 | Show Equation

Position Equation s(t) =

Plot your s vs. t graph with scales; label your axes including units

Use your graph to estimate the time it will take to hit the ground = sec

From your s(t) equation use calculus to find the velocity function v(t) =
Plot v vs. t graph with scales; label your axes including units

Use your graph to estimate the velocity at the instant the ball hits the ground   =                              m/s

Find the acceleration of the ball. a(t) =                  m/s² or ft/s²
Find the difference between your experimental acceleration and earth's g = 9.81m/s² or g = 32ft/s²

Optional: Find the % error = difference/9.81 X 100% =

*Alternatively you can go here to do a quadratic regression (opens in new window):
www.colby.edu/chemistry/PChem/scripts/lsfitpl.html

Input data; Use the "Fit & Plot" function" shown here. If c is blank, put 1.