Question

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, theta 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, theta, and H, and the other that allows you to solve for x in terms of k, m, g, theta, and v.

Answer 1

Did you attempt to use F=ma and the motion equations?

Answer 2

Yes, I've attempted several equations, including some from Wikipedia, but nothing has worked out so far ): I don't know how to derive the equations - wikipedia offers some, but it's confusing and skips a few steps in explaining.

Answer 3

My advise though is to know what you're looking for.
You want to know far it will go, so you'll need to know the velocity.
If you want to know the velocity, you'll have to know the acceleration.
If you want to know the acceleration, you'll have to know the force applied.
If you want to know the force applied, you'll have to understand F=ma.
Okay, I will give a few steps.
Taking the F of spring ,
by Newton's second law,
\[F_{s} = ma\]
Where by hooke's law, \[F_{s}=kx\]
So, \[kx=ma \]
arranging,
\[a=\frac{ kx }{ ? }\]
Now, you 've got the acceleration.
Are you familiar with the three motion equations?

Answer 4

sorry, \[a=\frac{ kx }{ m }\]

Answer 5

Now, this is where there is no gravity. I believe you can now derivate the equaion where it is in a gravitational field?

Answer 6

The three motion equations as in \[F1 = F2\] , \[E1 = E2\], and \[P1 = P2\]? Or as in \[d = v1t + 1/2(a(t^2))\], \[Vf^2 = Vi^2 +2ad\], the like?

Answer 7

I've started on the second equation, to get \[1/2kx^2 + mgy1 = 1/2mv^2 + mgy2\]

Answer 8

at least so far... I'm clearly over my head here.

Answer 9

ok I'm starting to get a handle on the first equation. So...
I've got \[x = vcos thetat\] and \[y = vsin \theta t - 1/2g t^2\]