Answer:
Approximately [tex]71\%[/tex].
Explanation:
The formula for the kinetic energy [tex]\rm KE[/tex] of an object is:
[tex]\displaystyle \mathrm{KE} = \frac{1}{2}\, m \cdot v^2[/tex],
where
- [tex]m[/tex] is the mass of that object, and
- [tex]v[/tex] is the speed of that object.
Important: Joule ([tex]\rm J[/tex]) is the standard unit for energy. The formula for [tex]\rm KE[/tex] requires two inputs: mass and speed. The standard unit of mass is [tex]\rm kg[/tex] while the standard unit for speed is [tex]\rm m \cdot s^{-1}[/tex]. If both inputs are in standard units, then the output (kinetic energy) will also be in the standard unit (that is: joules,
Convert the unit of the arrow's mass to standard unit:
[tex]m = 63\; \rm g = 0.063\; \rm kg[/tex].
Initial [tex]\rm KE[/tex] of this arrow:
[tex]\begin{aligned}\mathrm{KE} &= \frac{1}{2} \, m \cdot v^2 \\ &= \frac{1}{2}\times 0.063\; \rm kg \times \left(\rm 28 \; m \cdot s^{-1}\right)^2 \\ &\approx 24.696\; \rm J\end{aligned}[/tex].
That's the same as the energy output of this bow. Hence, the efficiency of energy transfer will be:
[tex]\displaystyle \frac{24.696\; \rm J}{34.8\; \rm J} \times 100\% \approx 71\%[/tex].
