Calculating the Speed of an Object Launched by a Spring Catapult

[johnsholto]

A spring catapult consists of a massless spring and a massless cup. An object of a certain mass is loaded into the cup, the spring is extended to a length L, and the object is launched horizontally.

What is the speed of the object?

s is the natural length of the spring, L is the length the spring was extended to. their difference is the extension length x

E=0.5mv^2 and E=0.5kx^2 -> v=√(k(L-s)^2/m)

Now what about vertically? I assume that the speed would be less since there is the gravitational potential that changes as the spring returns to its natural length. Might the answer then be:

E=0.5mv^2 and E=0.5kx^2-mg(L-s) -> v=√[k(L-s)^2-2mg(L-s)]/√m

 

[LawrenceC]

It looks correct but why not use x instead of L-s? Also, I would remove sqrt(m) from denominator as it makes the expression easier to dedipher.