determine velocity using conservation of energy?

Question

A block, mass 0.75 kg, is "shot" from a spring gun from a table. The table has a height 1.04 m and is frictionless. If the spring has k=28 N/m and is originally compressed 0.23 m, how fast will the block be goign when it hits the ground?


(1/2)*kx^2 = (1/2)mv^2 ?????????????



I got 4.3 m/s but the answer is 4.73 m/s

Answer 1

The spring just gives it initial velocity
(1/2)*kx^2 = (1/2)mu^2 here u is intial velocity

u^2 = (k/m) x^2 ---(1)
final velocity V when hits ground

v^2 = u^2 + 2gh
v^2 = (k/m) x^2 + 2gh

v^2 = (28/0.75) (0.23)^2 + 2*9.8*1.04

v^2 = 1.974 + 20.384 = 22.358

V= 4.728 m/s