Question

the diagram shows a person holding a bow and arrow. which will most likely increase the kinetic energy in this system? pulling farther back on the string releasing the string holding the arrow higher decreasing the mass of the arrow

Explanation:

Step1: Analyze the effect of pulling farther back on the string

Pulling farther back on the string stores more elastic potential energy in the bow. When the string is released, this potential energy is converted into kinetic energy of the arrow. But just pulling farther back (before release) doesn't directly increase the kinetic energy of the system in motion.

Step2: Analyze the effect of releasing the string

When the string is released, the elastic potential energy stored in the bow (from pulling it back) is converted into kinetic energy of the arrow. As the arrow moves, its kinetic energy \(K = \frac{1}{2}mv^{2}\) (where \(m\) is mass and \(v\) is velocity) increases.

Step3: Analyze the effect of holding the arrow higher

Holding the arrow higher increases its gravitational potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height), not its kinetic energy.

Step4: Analyze the effect of decreasing the mass of the arrow

The formula for kinetic energy is \(K=\frac{1}{2}mv^{2}\). If we assume the velocity \(v\) (at the moment of release, the conversion of potential to kinetic energy per unit mass) is related to the initial pull (for a given pull, the energy transfer per unit mass). But a lower mass \(m\) with the same energy transfer (from potential to kinetic) would mean \(v=\sqrt{\frac{2K}{m}}\) (if \(K\) is considered as the energy from the bow - string system). However, the main source of kinetic - energy increase in the system (arrow in motion) is the release of the string which allows the conversion of stored potential energy (from pulling the bow) into kinetic energy.

Answer:

releasing the string