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.