Question

An arrow of mass 0.0306 kilograms is placed on a bow, and the string is drawn back 0.591 meters with an average force of 141 newtons. With what speed does the arrow leave the bow? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

`\begin{gathered} m=0.0306\text{ kg} \\ F=141\text{ N} \\ x=0.591\text{ m} \\ v=\text{?} \\ F=ma \\ \text{Solving a} \\ a=(F)/(m)=\frac{141N}{0.0306\text{ kg}}=4607.8m/s^2 \\ v^2=v^2_o+2ax \\ The\text{ arrow stars from rest},hence_{} \\ v_o=\text{ 0 m/s} \\ v^2=2ax \\ v=√(2ax) \\ v=\sqrt{(2)(4607.8m/s^2)(0.591\text{ m})} \\ v=73.8\text{ m/s} \\ \text{The spe}ed\text{ is }73.8\text{ m/s} \end{gathered}`