I had a physics lab where I had to build a sling shot sort of devices on a ramp. Basically, I have a ramp, with two springs attached on the end and the two strings are attached to a piece of wood. I put something in front of the piece of wood, pull the wood back, and let go. This launches the projectile.
What I am having trouble with is deriving equations. Here's what I mean:
This is directly from the assignment:
Derivation: Derive a set of equations to use to determine how far back (x) you need to pull a mass, m, in your slingshot to launch it a distance R. Your derivations will also include the spring constant, k, acceleration due to gravity, g, the launch angle, θ, and the height at which the projectile is launched, H. You should obtain 2 equations: One that gives the launch speed, v, in terms of R, θ, and H, and the other that allows you to solve for x in terms of k, m, g, θ, and v. Leave values in your equations as variables. On launch day you will plug in the values as needed. You will know k from your lab. R, and m you will be given on launch day. You can choose any value for θ that you desire. You will be able to calculate a value for v from the first equation to use in the second one.
The problem is, I don't know how to derive the equations. Here's some information I have from testing:
Launching a 270 g object takes 1.76 sec to hit the ground. Also, the distance it traveled horizonatally was 1.4 m. Other information for the ramp is in the diagram. K value and such is unknown. X value when launched was 10 cm for above information.