Final answer:
The velocity of the arrow is found using the work-energy principle, assuming 100% conversion efficiency from the force applied across a distance to the bow into kinetic energy. The resulting velocity when the archer releases the bow is approximately 79.3 m/s.
Step-by-step explanation:
The student's question is about finding the velocity of an arrow immediately after it is released from a bow, assuming 100% energy conversion efficiency from the work done by the archer to the kinetic energy of the arrow.
To solve this, we use the work-energy principle. Work done by the archer, W, is calculated by multiplying the force, F, applied to the bow by the distance, d, over which it is applied: W = F * d. Assuming 100% efficiency, this work is equal to the kinetic energy (KE) of the arrow: KE = 0.5 * m * v^2, where m is the mass of the arrow and v is its velocity. We can set W equal to KE and solve for v:
- W = F * d
- KE = 0.5 * m * v^2
- F * d = 0.5 * m * v^2
- v = sqrt((2 * F * d)/m)
Plugging in the values given in the question, we get:
- F = 182 N
- d = 0.38 m
- m = 0.022 kg
- v = sqrt((2 * 182 N * 0.38 m) / 0.022 kg)
- v = 79.3 m/s (expected rounded value)
The velocity when the archer releases the bow is approximately 79.3 m/s, given that the conversion of energy is 100% efficient.