An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?
In order to watch this solution you need to have a subscription.
This is Giancoli Answers with Mr. Dychko. The change in kinetic energy of this arrow is equal to the net force on it times its displacement. Now, there's 2 forces technically; there's gravity downwards and then there's the force to the right exerted by the bow. But gravity is going to be so small, it's really just negligible so we can ignore it and we'll consider the net force to be just the force of the bow. So kinetic energy can also be written as one-half, m, mass times velocity final squared minus one-half m v i squared. But it starts from rest and so we just have one-half m v f squared. So we can say, one-half m v f squared, which is change in kinetic energy is going to equal, F net times displacement since it's also equal to change in kinetic energy. And we'll rearrange this here for v f. So we'll multiply by 2 over m, and take the square root of both sides, and we have the final speed then is the square root of 2 times 105 newtons—force exerted by the bow—times 0.75 meters over which the bow is applying that force on the arrow. And divide by 0.085 kilograms— mass of the arrow— and so it will have a final speed of 43 meters per second.
Find us on:
