Projectile Uncertainty#

In the second PHYS 111 lab, Ahmed repeatedly launched a metal sphere and measured the horizontal distance $d$ it traveled. The launch angle was $\theta$ and the sphere was fired from a height $h$ above the ground. Using the measured value of $d$ and the known values of $g$, and $h$, Ahmed could determine the launch speed $v_0$ of the projectile. However, the expression for $v_0$ in terms of $d$, $g$, $\theta$, and $h$ was complicated! Things get quite a bit simpler if $h=0$. In this case:

Suppose that, with $h=0$, Ahmed and their lab partner make 30 measurements of $d$. Ahmed then determines that the average and standard deviation of their 30 measurements were $\overline{d}$ = 0.126 $m$ and $\sigma$= 0.053 $m$, respectively.