Calculating the Speed of a Ball Shot from a Spring Gun

[cstout]

Homework Statement

A spring gun (k = 28 N/m) is used to shoot a 56-g ball horizontally. Initially the spring is compressed by 18 cm. The ball loses contact with the spring and leaves the gun when the spring is still compressed by 12 cm. What is the speed of the ball when it hits the ground, 1.4 m below the spring gun?

Homework Equations

horizontal velocity, vertical velocity, Kinetic energy

 

[mgb_phys]

Assuming no energy is lost to friction you have two sources of energy.
1, The energy from the spring = force * distance.
2, The gravitational energy of falling the 1.4m = m g h

Both of these will be converted into kinetic energy of the particle = 1/2 m v^2
from this you can get the final speed.

 

[cstout]

is the distance the change in the compression of the spring for the energy of the spring?

 

[mgb_phys]

Yes - the energy stored in a spring is 1/2 K x^2
where K is the spring constant and X is the distance you compress it.

 

[cstout]

i got .0504 for the spring energy and 768.32 for the gravitational potential energy.
but then what equation or steps do i use to convert those into kinetic energy to get the final velocity

 

[mgb_phys]

Check your units!
You just add the spring energy and potential energy to get the kinetic energy.