A spring is pulled back and launches a ball. The ball flies into the air at a perfectly horizontal angle. How far will the ball go before it hits the ground?
Variables for the FINAL equation are:
∆x - distance the spring is pulled back
g - acceleration of gravity
m - mass of the ball
k - spring constant
∆R - range the ball will fly
h - height above the ground at the point that the ball passes the end of the launcher
1/2mv^2 - kinetic energy
1/2kx^2 - elastic potential energy
v=√(kx^2/m) - velocity derived from the kinetic energy equation
The Attempt at a Solution
I broke it up into 2 separate parts, one dealing with conservation of energy and the spring, and the other dealing with kinematics and the projectile motion of the ball in the air. I managed to find the velocity of the ball when it leaves the launcher, but beyond that I really had no idea where to go, as I need to find some way to eliminate both the velocity and time variables from the final equation, which would be much easier to use if I was able to.