# An archer puts a 0.39 kg arrow to the bowstring. An average force of 196.3 N is exerted to draw...

## Question:

An archer puts a 0.39 kg arrow to the bowstring. An average force of 196.3 N is exerted to draw the string back 1.28 m. The acceleration of gravity is 9.8 m/s 2 . Assuming no frictional loss, with what speed does the arrow leave the bow? Answer in units of m/s

## Conservation Of Energy :

In the conservation of energy the energy remains conserved during conversion from one form into another for example when the person is sitting on the top of the hill then the energy that it posses will be the potential energy but as soon as he jumps the potential energy starts converting into the kinetic energy keeping the mechanical energy constant.

Given

Mass of the arrow is {eq}m=0.39\ kg {/eq}

Average force exerted is {eq}F=196.3\ N {/eq}

Distance by which the string is pulled is {eq}S=1.28\ m {/eq}

Now for the work done in order to pull the string back :

{eq}W=F\times S\\ W=196.3\times 1.28\\ W=251.2\ J {/eq}

Now the work done will be converted into kinetic energy as soon as the arrow is released:

{eq}W=\frac{1}{2}mv^2\\ 251.2=\frac{1}{2}(0.39)v^2\\ v=35.89\ m/s {/eq}

Thus, the speed by which the arrow leaves the arrow is 35.89 m/s 