Maths B

Task 1.

a). INSERT COMPLETE GRAPH

The ball quickly reaches the highest point which is closest to the CBR. The displacement then increases as gravity acts upon the ball, moving it away from the CBR unit and thus increasing the displacement. This time - displacement graph mimics a parabolic function.

b).

This region (shown below) has been selected since the region 0.83 < x < 1.39 is irrelevant due to the ball being stationary or having its motion interrupted.

A quadratic regression was selected as a model for this data since motion involving gravitational forces ideally mimic parabolic functions when investigating distance - time graphs.

A quadratic model was found by using the TI-83 to generate a "Quadreg" of the selected data. This was then plotted against the given data and the two curves were compared.

Quadratic model:

Y = 1.4203 x2 - 1.8775 x + 0.9810

INSERT GRAPH OF QUADRATIC MODEL WITH DATA ON SAME GRAPH

The quadratic model generated fit's the data perfectly for this given region. This is due to the selection of the relevant domain, focussing only upon the ball as it experiences gravitational acceleration. The one downfall of this model is that the quadratic function does not cease increasing, unlike the data which it is modelled for. Therefore for value x > 1.35 the model values are irrelevant.

c).

Derivative of the Quadratic model:

dY / dT = 2.8406 x -1.8775

Task 2.

a).

The ball firstly is stationary, then is dropped from this height where it quickly travels away from the CBR unit. This can be seen by the increase on the velocity - time graph. The ball then hit's the ground, which is displayed on the graph as the very quick drop in the