Given data:
* The mass of the dart is m = 0.025 kg.
* The speed of the dart is v = 13 m/s.
Solution:
(a). The work done by the dartboard to stop the dart is,
![W=(1)/(2)mv^2](https://img.qammunity.org/2023/formulas/physics/college/u5a90cu12wccb8he7jigqop7non3us89bg.png)
Substituting the known values,
![\begin{gathered} W=(1)/(2)*0.025*13^2 \\ W=2.1125\text{ J} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/8fyg5gkfcqwpfphzkq79djcgq4uwf87zvf.png)
Thus, the amount of work done by the dartboard is 2.1125 J.
(b). As the friction of dartboard