homework help?

Question

a person does 100j of work in pulling back the string of a bow. what will be the imitial speed of a .5 kg arrow when its fired from the bow?

400m/s
200m/s
50m/s
20m/s

Answer 1

1/2mv^2= Kinetic Energy

so if you are converting those 100 joules to kinetic energy...
sqrt(100*2/m)=20m/s

Answer 2

E = [1/2]mV^2; V^2 = 2E/m = [2x100]/0.5 = 400
So V = sqrt(400) = 20 m/s. Whatever work you have done is stored in the arrow and the bow. When you release the arrow this gets converted into the kinetic energy of the arrow and the potential + kinetic energy of the bow and bow string because it vibrates a little. Neglecting all this energy transferred to the bow and thinking that the whole 100 J energy gets converted to kinetic energy of the arrow alone, we get the above result. If we do the actual experiment, the velocity of the arrow would be slightly less than 20 m/s.

Sorry! I gave bad rating to Pluto by mistake; his answer was correct in principle!