BC Banner

Free Fall


A ball is dropped and it’s height, in feet, and it’s corresponding time, in seconds, is recorded by a CBR motion detector.


Time 0 0.043 0.086 0.129 0.172 0.215 0.258
Height 2.5 2.436 2.345 2.233 2.1 1.959 1.795


Can we find a quadratic function to model this data?


How far does the object fall in t seconds?


The data “looks” like a parabola, so we will try to fit a quadratic model




Choosing three data points and substituting them into the quadratic model will generate a system of three linear equations in the variables a, b, and c.


The system can be reduced to this simpler system.


Solution: From the solution of this system, we can write the quadratic model.




AMATYC Logo About Us | Contact Us | ©2010 AMATYC