rollingcan

Rolling Can

Introduction: In this investigation we modelled the distance of a can from a sensor when the can rolls up and back down a small slope. We used the data from the sensor to create an equation to model the distance of the can.



From our graph, we choose 3 points from the quadratic curve, and used the Matrix method to calculate the equation. First point: (1.0215055, 0.44104064) Second point: (1.2903224, 0.58080069) Third point: (1.505376, 0.6287321)

y = ax2 + bx + c 0.44104064 = 1.0215055^2 a + 1.0215055 b + c 0.58080069 = 1.2903224^2 a + 1.2903224 b + c 0.6287321 = 1.505376^2 a + 1.505376 b + c

Matrix formula: [1.0434734865303 1.0215055 1 0.44104064] [1.6649318959418 1.2903224 1 0.58080069] [2.266156901376 1.505376 1 0.6287321]

In calculator: [1.0434734865303 1.0215055 1 0.44104064] rref ( [1.6649318959418 1.2903224 1 0.58080069] ) [2.266156901376 1.505376 1 0.6287321]

= ( [1 0 0 -0.6138558739] [0 1 0 1.93903711] [0 0 1 -0.899154104] )

Equation:
 * y = -0.6138558739 x^2 + 1.93903711 x + -0.899154104**

Double Checking, we inputted the data in STAT, and used quadreg to derive an equation.
 * y = -0.6138558739 x^2 + 1.93903711 x + -0.899154104** (same equation)

Conclusion: We used two methods to find out the equation for the quadratic shape. We used the matrix method with three points, and double checked with calculator regression. As we started rolling the can a second or two after the recorder started, the equation appears to not start at (0,0). Instead, the graph starts at (.564,0), and the range for this graph is .564 < x < 2.6 (which are the roots).