# Motion and g

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Theory
The aim of this experiment is to investigate the one dimension motion of an object so as to obtain the acceleration due to gravity, g. The object used in the experiment is a basketball which is dropped from a parking garage and then below a sonic ranger. Since acceleration is a function of both the displacement and the time taken, then the acceleration due to gravity can be estimated using the height of the ball and the falling time according to the relationship give as;

g=2y/t^2

Where y is the height that the ball falls, t is the time taken for the ball to reach the ground and g is the acceleration due to gravity. The ball was allowed to fall for about seven times to allow for error analysis and hence the accuracy of the obtained value. The second part involved dropping the ball under the sonic ranger and letting the Logger Pro software to plot the velocity-time graph. The acceleration due to gravity is in this case estimated to be the gradient of the linear part of the graph.

Error Analysis
The g values obtained in the two instances are compared from the standard value of g which is globally accepted as 9.81m/s2 to establish the percent error. The percent error in the parking garage experiment yielded 35.79% while that of the sonar ranger yielded 0.6728%. The high percent error in the parking garage experiment was due to systematic errors evident from the wild fluctuations of the g values in the seven trials. The systematic errors might be due to the air friction as the ball fell and the inaccuracy in time measurements. The error can be reduced by having the experiment in an air tight environments such as vacuum chambers as well as having several participants measure the time and obtaining the average. The sonic ranger had a lower percent error due to the small falling height hence lesser effect of friction.

Expansion
The measurement of time was highly sensitive as it caused a wild variation of g in parking garage experiment. This is because, as shown in the experiment, g varies inversely proportional to the square of time. A small change in time would therefore cause a significant change in the value of g.

Supposing the measurement of time is off by a tenth of a second then the new values of g would be;

 Original Time (seconds) New Time (seconds) Old New 1.38 1.37 11.76 11.93457 1.0 0.99 22.4 22.85481 1.16 1.15 16.64 16.93762 1.33 1.32 12.66 12.85583 1.29 1.28 13.4607 13.67188 1.39 1.38 11.5936 11.76223 1.26 1.25 14.1093 14.336

The new value of g 14.90756〖m/s〗^2 and hence the percent error becomes 51.96%.