A 0.069-kg arrow is fired horizontally. The bowstring exerts an average force of 65 N on the arrow over a distance of 0.95 m. With what speed does the arrow leave the bow?

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To find the speed at which the arrow leaves the bow, we need to use the concept of work and energy. The work done on an object can be calculated using the formula:

Work = Force × Distance

In this case, the force exerted by the bowstring is 65 N, and the distance over which this force is applied is 0.95 m. Therefore, the work done on the arrow is:

Work = 65 N × 0.95 m = 61.75 Joules

According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the arrow results in it gaining kinetic energy. Therefore, we can write:

Kinetic Energy = 61.75 Joules

The kinetic energy of an object can be calculated using the formula:

Kinetic Energy = 0.5 × mass × velocity^2

In this case, the mass of the arrow is 0.069 kg, and we need to find the velocity at which it leaves the bow. Rearranging the equation, we have:

Velocity^2 = (2 × Kinetic Energy) / mass

Substituting the values, we get:

Velocity^2 = (2 × 61.75 Joules) / 0.069 kg

Simplifying the equation, we get:

Velocity^2 = 1807.24

Taking the square root of both sides, we have:

Velocity = √1807.24

Velocity ≈ 42.51 m/s

Therefore, the arrow will leave the bow with a speed of approximately 42.51 m/s.