Determining Compression of a Spring involving Spring Constants

[gomess]

Homework Statement

A 10g marble is launched horizontally from a spring of K = 20 N/m. If the marble ended up with a launch speed of 40m/sec, how much (in cm) was the spring compressed by?

Homework Equations

F=kx
E=\frac{1}{2}kx^2

The Attempt at a Solution

To find how much the spring was compressed by, I know that you must solve for x in either equation. But I am unsure what values F or E would be. F =ma, but no acceleration, displacement, or time interval is given. ΔE= FΔd, but still force is required.

 

[rock.freak667]

The elastic potential energy of the spring when compressed to a distance 'x' will be converted into kinetic energy.

Do you know how to find the kinetic energy of an object given its mass and velocity?

 

[gomess]

\frac{1}{2}mv^2 = \frac{1}{2}kx^2

(0.01)(0.4)^2 = 20x^2

0.0089 m = x

8.9 cm = x

I wrote that the initial velocity was 40m/s, should have been 40cm/s. Would this solution be correct though?