Spring launcher on incline hitting elevated target

[michael simone]

Homework Statement

A spring of mass “m” is put on a launcher elevated at “θ” degrees above the horizontal. It is pull back a distance “x” and launched at a target that must travel vertically “dy“ and a horizontal distance of “dx”. The spring has a constant of “k”.Derive an equation (or series of equations) given m, θ, dy ,dx, k so you can calculate a value of x.Example The target is 3.5 m away and the launder is elevated at 30o and it is 1.2 m high, the mass of the spring is 4.5 g, what distance should the spring be pulled back to land in a target that is 0.40 m tall if k = 18 N/m?

Homework Equations

PTi= PTf
Ei=Ef
ENERGY
KINETIC (Ek)
Ek=1/2 MV^2
SPRINGS(elastic Ee)
Ee=1/2 KX^2
E1=E2 IE
Potential (Eg)
Eg= mgh or mg(delta y)
vx= vicos (theta)
Projectile motion and Energy[/B]

The Attempt at a Solution

 

[Dr Dr news]

Check your textbook for 1) 2D trajectory equations and 2) the conservation of mechanical energy. You will need both.

 

[michael simone]

Check your textbook for 1) 2D trajectory equations and 2) the conservation of mechanical energy. You will need both.

ENERGY
KINETIC (Ek)
1/2 MV^2
SPRINGS(elastic Ee)
1/2 KX^2
E1=E2 IE
Potential (Eg)
mgh or mg(delta y)
vx= vicos (theta)

 

[Dr Dr news]

The classical range equation is based on the initial elevation and the final elevation both being on the ground. In your problem you have an initial height as well as a final height which means you need to carry them along in your trajectory analysis.

 

[michael simone]

thanks for that tip, but how do i slove this when v is not provided.

 

[haruspex]

thanks for that tip, but how do i slove this when v is not provided.

Are you familiar with the SUVAT equations for constant acceleration?
https://en.wikipedia.org/wiki/Equations_of_motion