A 15g ball is shot from a spring gun whose spring has force constant of 600N/m. The spring is compressed by 5cm. What is the greatest possible horizontal range of the ball for this compression is (take g=10m/s^2)?
The energy stored in the spring is given by:
k is the force constant.
x is the extension.
I will assume that all this energy will appear as the kinetic energy of the ball:
I will assume that the ball is being launched from the ground as no height is given. The range is given by:
Using The Chain Rule:
This is the launch angle that gives the maximum range.
Using this value gives: