# Work Energy Theorem of a fired arrow

1. Dec 8, 2008

### Notyou

1. The problem statement, all variables and given/known data
A 0.065 kg arrow is fired horizontally. The bowstring exerts an average force of 70 N on the arrow over a distance of 0.90 m. With what speed does the arrow leave the bow?

2. Relevant equations
W=Fd
W=KE final - KE initial
KE= 1/2mv^2

3. The attempt at a solution
First I used the force given and the distance given and found the work to be 63J. From there I set that equal to the change in kinetic energy. I believe the final kinetic energy is 0, but if that is the case I am obtaining the wrong answer. The final answer is supposed to be 44 m/s.

2. Dec 8, 2008

### PhanthomJay

It's initial KE is zero, but why do you expect its KE as it leaves the bow to be zero? It leaves it with a certain speed, and KE is associated with that speed.

3. Dec 8, 2008

### Notyou

Hmm... I suppose with KE final I assumed it meant when the arrow hits the ground. So... I had it backwards? Did I just interpret the question wrong?

4. Dec 8, 2008

### Notyou

Oh geeze, I just figured out what I did wrong. I wrote it down as .65 instead of .065. Thank you a lot for your help!

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