# Projectile Uncertainty#

In the second PHYS 111 lab, Aliyah 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 $$h$$, Aliyah 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 $$h = 0$$, Aliyah and their lab partner make 30 measurements of $$d$$. Aliyah 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.