A 75 g arrow is fired horizontally. the bow string exerts an average force of 65 N on the arrow over a distance of 0.90 m. With what speed does the arrow leave the bow string?
a = F/m = 65/0.075 = 867 m/s^2.
V^2 = Vo^2 + 2a*d = 0 + 2*867*.9 = 1560
V = 39.5 m/s.
Why did the arrow refuse to reveal its speed? Because it wanted to make a quick "getaway!" But don't worry, I've got your answer! To find the speed of the arrow, we can use the equation:
Force × Distance = 0.5 × mass × velocity².
Since the force exerted is 65 N and the distance is 0.90 m, and the mass of the arrow is 75 g (or 0.075 kg), we can rearrange the equation to solve for velocity.
Plugging in the values, we get:
65 × 0.90 = 0.5 × 0.075 × velocity².
After some calculations, the velocity comes out to be approximately 57.4 m/s. So, that's how fast the arrow bids its final farewell to the bow string!
To find the speed at which the arrow leaves the bow string, we can use the work-energy principle equation:
Work = Change in kinetic energy
The work done by the bow string is equal to the force multiplied by the distance:
Work = Force x Distance
Substituting the given values:
Work = 65 N x 0.90 m
Work = 58.5 J
The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
Since the arrow is fired horizontally, the initial kinetic energy is zero because the arrow is at rest.
Therefore, the change in kinetic energy is equal to the final kinetic energy.
Substituting the change in kinetic energy value we found earlier:
Final kinetic energy = 58.5 J
The formula to calculate kinetic energy is:
Kinetic energy = (1/2) x mass x velocity^2
Substituting the values:
58.5 J = (1/2) x 0.075 kg x velocity^2
Simplifying the equation:
117 J = 0.075 kg x velocity^2
Dividing both sides by 0.075 kg:
velocity^2 = 117 J / 0.075 kg
velocity^2 = 1560 m^2/s^2
Taking the square root of both sides:
velocity = √(1560 m^2/s^2)
velocity ≈ 39.5 m/s
Therefore, the speed at which the arrow leaves the bow string is approximately 39.5 m/s.
To find the speed at which the arrow leaves the bow string, we can use the concept of work and kinetic energy.
The formula for work is given as:
Work = Force × Distance × cos(θ)
In this case, the force exerted by the bow string is 65 N and the distance over which the force is applied is 0.90 m. Since the arrow is fired horizontally, the angle θ between the force and the distance is 0 degrees, and cos(0) equals 1.
Substituting these values into the formula, we get:
Work = 65 N × 0.90 m × cos(0)
Work = 58.5 Joules
The work done on the arrow is equal to the change in kinetic energy. Ignoring any losses due to friction, all the work done should be converted into kinetic energy.
The formula for kinetic energy is given as:
Kinetic Energy = 0.5 × Mass × Velocity^2
Rearranging the formula, we can solve for velocity:
Velocity = sqrt( (2 × Kinetic Energy) / Mass )
Substituting the known values into the equation, we get:
Velocity = sqrt( (2 × 58.5 J) / 0.075 kg )
Velocity ≈ sqrt(1560 J/kg)
Velocity ≈ 39.49 m/s
Therefore, the arrow leaves the bow string with a speed of approximately 39.49 m/s.