Final answer:
The mass of the arrow is calculated by using the kinetic energy formula. After rearranging the formula to solve for mass and substituting the given kinetic energy and velocity into it, the mass is found to be approximately 0.02 kg or 20 grams.
Step-by-step explanation:
To find the mass of an arrow given its kinetic energy and speed, you can rearrange the kinetic energy formula. The formula for kinetic energy (KE) is KE = 0.5 × m × v^2, where m is the mass of the object and v is its velocity. We are given that the kinetic energy is 45 J and the velocity is 67 m/s. Substituting these values into the formula and solving for m, we can find the mass of the arrow.
First, rearrange the formula to solve for mass: m = (2 × KE) / v^2. Then substitute the provided values: m = (2 × 45 J) / (67 m/s)^2. Calculating this yields the mass of the arrow, which can be rounded to two decimal places for ease of understanding.
Therefore, the mass of the arrow is:
m = (90 J) / (4489 m^2/s^2)
m ≈ 0.02 kg, or 20 grams.