Spring toss?

Question

I must come up with an equation the determine the distance a spring must be pulled back on a ruler, for it to launch off an hit a specific target. The ruler can be at any angle, the top of the spring is hooked onto the top of the ruler and when you pull back an let go the spring is supposed to fly off and hit the target.

I know Hookes law must be used F=kx, as well as F=ma, and then likely one of the acceleation equations, but I dont know how to put them all together.

Thanks in advance.

Answer 1

The initial velocity can be found from the mass and stiffness of the spring and how far you pull it back. The potential energy in the stretched spring, kx^2/2 = the kinetic energy of the moving spring = mv^2/2. From v and the launch angle you can predict the trajectory of the spring using standard ballistic equations (see ref.).