Calculate Arrow Velocity from Stored Energy

[KingBigness]

Homework Statement

If the extension of the bow is 5.5 cm and you have determined that this corresponds to 305 mJ , what is the velocity with which a 15 gm arrow will leave the bow if 64 percent of the stored energy is transferred to the arrow?
Calculate the velocity in m/s but do not include the units in your answer.

Homework Equations

none

Please help!

 

[Fewmet]

Homework Statement

If the extension of the bow is 5.5 cm and you have determined that this corresponds to 305 mJ , what is the velocity with which a 15 gm arrow will leave the bow if 64 percent of the stored energy is transferred to the arrow?
Calculate the velocity in m/s but do not include the units in your answer.

Homework Equations

none

Please help!

This is a problem in the conservation of energy. The potential energy stored in the bow ends up as kinetic energy of the arrow (or, in this case, 64% of it ends up as kinetic energy of the arrow).

So what is the kinetic energy of the arrow?

Do you see how to use the mass and the energy to find the velocity of the arrow? (Be careful to keep units consistent.)

 

[KingBigness]

So can i use FD=0.64(1/2mv^2)

 

[KingBigness]

wait...thats not right...0.64FD=1/2mv^2?

 

[Fewmet]

wait...thats not right...0.64FD=1/2mv^2?

That'll do it.