Lab 3 Calculating averages there error and the horizontal ve

Lab 3 Calculating averages, there error and the horizontal velocity. In this experiment we do each launch 3 times and measure 3 values of the times the ball passes through the photo gates (t1,t2, t3) and the distance the ball travels (X1, x2, X3). If for one launch we got the following data Calculate me average time and distance and the errors in both averages using equations 1.5 and 1 5b. If the effective diameter of the ban is 0 014 +/ 0.001 m what is the horizontal velocity of the ball and its error (You need to use equation 1.7 from lab 1 for the error).

Solution

t_avg = (0.0171 + 0.0172 + 0.0177)/3 = 0.0173 s
t_avg = [((0.0171-0.0173)² + (0.0172-0.0173)² + (0.0177-0.0173)²)/3] = 0.000265 s

x_avg = (0.34 + 0.324 + 0.32)/3 = 0.328 m
x_avg = [((0.34-0.328)² + (0.324-0.328)² + (0.32-0.328)²)/3] = 0.00864 m

v_x = 0.014/0.0173 = 0.809 m/s

v_x = 0.809[(0.001/0.014)² + (0.000265/0.0173)²] = 0.059 m/s