# Definition of Success problems with projectile motion

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1. Oct 5, 2016

### Minestra

So I just got beat up by this question on my midterm. I'm not sure if these problems are always called definition of success but that is how my professor refers to them as.

The question: (paraphrased)

When you walk into your dorm room you like to throw your keys onto the center of your desk. The center of your desk is 8 meters from you and is 1 meter high. You're nearly 2 meters tall thus your throw well start at 2 meters. You throw it at an angle of 30 degrees. Because of all your practice it lands dead center on your desk. What is the initial Velocity, Vo, of your throw, and at what time, t, does it land?

My attempts and thoughts:

I was at a total loss for this problem, I tried reworking the three constant acceleration equations and got no where. Upon leaving the lecture hall, it dawned on me that the range equation may help but I'm not 100% on that either. Thanks for your help I just want to know how to approach this type of problem in the future.

2. Oct 5, 2016

### andrewkirk

Write two equations, one for height y above the floor and one for horizontal distance x from where you were standing.

The equations will involve $x,y,t,V_0$ as well as sines and cosines of the known angle 30 degrees. At the landing point we have $x=8,y=1$, which leaves us with two unknown variables and two equations, hence that can be solved.

3. Oct 5, 2016

### RUber

You are looking to find the velocity required to start at [0,0] with initial angle of 30 degrees and end at [8,-1].
Your horizontal component of velocity is ... ?
Your vertical component of velocity is ... ?
Using vertical component of velocity $v_{vert},$ you can determine the time it takes to return back to y = -1.
$r(t) = v_{vert}*t - 9.8 \frac{t^2}{2} = -1$
Take the positive option for t in terms of v_0.
Using the horizontal component $v_{horiz},$ you can set $r(t) = 8 = v_{horiz}*t$.
This will give you an equation in terms of the components of v.
The form you get should look just like the range equation, except some forms of the range equation assume that you will end at y=0. If that were the case, you simply shift your starting points accordingly.

4. Oct 6, 2016

### Minestra

Well theres 20 points I lost by writing Vox and Voy oppose to VoCOS(Theta) etc. Thanks for the response lesson learned.

5. Oct 6, 2016

### RUber

You were not wrong to use $V_{0x}, V_{0y}$, but the solution hinges upon how they are related to each other by the launch angle.