Final answer:
The speed of the arrow as it leaves the bow is approximately 44.2 m/s, calculated using the work-energy principle, where the work done by the bow on the arrow is equal to its change in kinetic energy.
Step-by-step explanation:
To determine the speed of the arrow as it leaves the bow, we can use the work-energy principle which states that the work done on an object is equal to its change in kinetic energy. The work done by the bow on the arrow can be calculated by multiplying the force exerted by the bowstring by the distance over which it acts.
The formula for work is: Work = Force × Distance.
In this case, the force is 110 N and the distance is 0.78 m, so the work done on the arrow is:
Work = 110 N × 0.78 m = 85.8 J
This is the kinetic energy the arrow has as it leaves the bow.
To find the arrow's speed, we use the formula for kinetic energy: KE = ½ mv², where m is the mass of the arrow and v is its speed. Solving for v gives us:
½ × 0.088 kg × v² = 85.8 J
v² = (85.8 J) / (0.044 kg)
v = √(1950)
v = 44.2 m/s (approx)
Therefore, the speed of the arrow as it leaves the bow is approximately 44.2 m/s.