Question

an arrow of mass .04 kg is pulled back 10 cm in the bow, having a force of 25.2 N. It is released 1.5m from the ground...how far will the arrow fly?
(all of the energy from pulling it back converts into the flying arrow)

Answer 1

This problem is missing information.

If the pull force is constant:
pulled 0.10 meters * 25.2 = 2.52 Joules
.5 m u^2 = 2.52 Joules
solve for u

however if the bow behaves like a spring

then average force = 1/2 * max force
and we get 1.26 Joules

You do not say which

If you fire horizontally
solve vertical problem to find time in air
(1/2) g t^2 = 1.5 meters
solve for t
then
horizontal distance = u t

If you fire up at 45 degrees (max range) it is a little more complicated but again solve the vertical problem for time, then do the horizontal problem for distance.