Calculate speed (work and energy)

[Physicsrapper]

A vertical spring with spring constant 300 N/m is compressed 0.06 m and a 0.25 kg ball placed on top. The spring is released and the ball flies vertically upward.

What is the ball's speed when it has gone 0.1 m high?

I don't know which relationship is required to find the speed, Can someone please help?
I calculated the maximum hight:
mgh = 1/2Dy^2
h = 0.22 m

Then i made use of the formula
E(final) = E(Initial)

0.25 * g * 0.22 = 0.25 * g * 0.1 + 1/2 * 0.25 * v^2
v = 1.53m/s

Is that correct?

 

[gneill]

Not sure why you went to the trouble of using the maximum height. All you really need is the total energy at any instant, so the spring potential energy alone would suffice if you take the zero-reference for gravitational PE to be the ball's pre-release position.

The only really questionable part of your solution is the vagueness of "0.1 m high" in the problem statement. Where's the height measured from? Is it the position of the ball before the spring is compressed, or the position of the ball when the spring is compressed?

 

[CWatters]

I don't know which relationship is required to find the speed...

Conservation of energy. The ball starts off with an initial KE that is converted into a combination of PE and KE on the way up. You can calculate the PE at any height (eg at 0.1M). The remaining energy is KE from which you calculate the velocity.