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:

\[v = \sqrt{\frac{gd}{2cos(\theta)sin(\theta)}}\]

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 \(\bar{d}\) = 0.126 \(m\) and \(\sigma\)= 0.053 \(m\), respectively.

Part 1

If g = 9.81 \(\frac{m}{s^2}\) and \(\theta\) = 30, what is the launch speed \(v_0\)?

Answer Section

Please enter in a numeric value in m/s.

Part 2

What is the uncertainty in your measured value of \(d\)?

Answer Section

Please enter in a numeric value in m.

Part 3

What is the uncertainty in the value of \(v_0\) that you determined? For this problem, assume that the launch angle is known to very high accuracy, such that its uncertainty can be neglected.

Answer Section

Please enter in a numeric value in m/s.

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.