Final answer:
The arrow leaves the bow with a speed of B. 32.1 m/s as calculated using the work-energy principle, where the work done by the bow is transformed into the kinetic energy of the arrow.
Step-by-step explanation:
To determine with what speed the arrow leaves the bow, we can use the work-energy principle. The work done by the bow on the arrow gives it kinetic energy, which we can calculate by the formula Work = Force × Displacement. Given that the bowstring exerts an average force of 89.0 N over a distance of 0.782 m, the work done on the arrow can be calculated as (89.0 N) × (0.782 m) = 69.618 joules. This work is equal to the kinetic energy of the arrow as it leaves the bow, which is given by the formula Kinetic Energy = (1/2) × mass × velocity2.
Therefore, we can set up the equation (1/2) × (0.0850 kg) × velocity2 = 69.618 joules. Solving for velocity gives us the speed of the arrow as it leaves the bow. Calculating this, we find that the arrow's speed is approximately 32.1 m/s, which matches with option B of the provided choices.
SUMUP: The arrow leaves the bow with a speed of 32.1 m/s.