a 27 g arrow is shot horizontally. the bowstring exerts an average force of 75 N on the arrow over a distance of 78 cm. detrmine the speed of the arrow as it leaves the bow.

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To determine the speed of the arrow as it leaves the bow, we can use the work-energy principle. The work done by the bowstring is equal to the change in kinetic energy of the arrow.

The work done by the bowstring can be calculated using the formula:

Work = Force x Distance

Given that the average force exerted by the bowstring is 75 N and the distance over which the force is applied is 78 cm (0.78 m), we can substitute these values into the formula:

Work = 75 N x 0.78 m

Work = 58.5 Joules

The change in kinetic energy of the arrow is equal to the work done by the bowstring. So, the change in kinetic energy is also 58.5 Joules.

The kinetic energy of an object is given by the formula:

Kinetic Energy = (1/2) x mass x (velocity)^2

Given that the mass of the arrow is 27 g (0.027 kg), and we need to find the velocity of the arrow, we can rearrange the formula to solve for velocity:

(1/2) x 0.027 kg x (velocity)^2 = 58.5 J

0.0135 kg x (velocity)^2 = 58.5 J

(velocity)^2 = 58.5 J / 0.0135 kg

(velocity)^2 = 4333.33 m^2/s^2

Taking the square root of both sides to solve for velocity:

velocity = √(4333.33 m^2/s^2)

velocity = 65.9 m/s

Therefore, the speed of the arrow as it leaves the bow is approximately 65.9 m/s.

To determine the speed of the arrow as it leaves the bow, we can use the work-energy principle. The work done on the arrow by the bowstring is equal to the change in the arrow's kinetic energy.

The work done can be calculated using the formula:

Work = Force * Distance

Given that the average force exerted by the bowstring is 75 N and the distance over which the force is exerted is 78 cm (or 0.78 m), the work done can be calculated as follows:

Work = 75 N * 0.78 m
Work = 58.5 Joules

Since the work done on the arrow is equal to the change in its kinetic energy, we can equate this to the kinetic energy formula:

Work = (1/2) * mass * velocity^2

Where mass is 27 g (or 0.027 kg).

58.5 Joules = (1/2) * 0.027 kg * velocity^2

Simplifying the equation:

58.5 Joules = 0.0135 kg * velocity^2

To find the velocity, we can rearrange the equation:

velocity^2 = 58.5 Joules / 0.0135 kg
velocity^2 = 4333.3 m^2/s^2

Taking the square root of both sides:

velocity = √(4333.3 m^2/s^2)
velocity ≈ 65.86 m/s

Therefore, the speed of the arrow as it leaves the bow is approximately 65.86 m/s.