# Need help finding initial minimum speed

1. Oct 11, 2009

### raytrace

1. The problem statement, all variables and given/known data
A bale ejector consists of two variable-speed belts at the end of a baler. Its purpose is to toss bales into a trailing wagon. In loading the back of a wagon, a bale must be thrown to a position 8 feet above and 16 feet behind the ejector. Find the minimum initial speed of the bale and the corresponding angle at which it must be ejected from the baler.

2. Relevant equations

$$r(t)=(v_{o}*cos\Theta*t)i + [h + (v_{o}*sin\Theta*t) - 16t^{2}]j$$

3. The attempt at a solution
Unfortunately the very beginning is where I'm stuck. I have two unknown that I am asked to solve (minimum initial velocity and the angle) and not sure how to start solving this. Could someone give me a nudge in the right direction on how to start?

2. Oct 11, 2009

### LCKurtz

I would start by placing the ejector at the origin so h = 0, and the "reverse ejection" direction in the positive x direction. So your target is at x = 16, y = 8. Then if you set x = 16, y = 8 you will have two equations in three variables, v0, t, and $\theta$. If you eliminate t between them that should give you an equation with v0 and $\theta$ to work with.

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