Question

An archer pulls back 0.75 m on a bow which has a stiffness of 200 N/m. The arrow weighs 50 g. What is the velocity of the arrow immediately after release?

• A. 48.9 m/s
• B. 47.4 m/s
• C. 50.0 m/s
• D. 45.0 m/s

Answer 1

The correct option is B 47.4 m/s

The bow can be treated as a type of spring. The potential energy of a spring is: $\left(\frac{1}{2}\right)$k$x^2$,
Therefore,the potential energy PE of the bow is:
PE = $\left(\frac{1}{2}\right)$(200)${0.75}^2$ = 56.25 J
The kinetic energy of a particle is $\left(\frac{1}{2}\right)$m$v^2$, The arrow can be treated as a particle since it is not rotating upon release.
Therefore, the kinetic energy KE of the arrow is:
KE = $\left(\frac{1}{2}\right)$(0.05)$v^2$
If we assume energy is conserved, then
PE = KE
Solving for the velocity of the arrow v we get
v = 47.4 m/s.