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Here is a fairly straightforward brainteaser that I hope you find useful for trying out the features and Apps on the HP Prime. I'm not so interested in exact answers, but more-so how you used the Prime to get you there. I have found some ways to explore this numerically, algebraically and graphically - along with a few dead ends.

Colonel Sanders needs to hit two targets at exactly the same time which are located on a hill almost 1km from his camp. He is down to one cannon and one aircraft, each with only one shell/bomb.

Cannon: Has one shell with a fixed 1000m max range and is located at fixed location (0,0)
Aircraft: Flying steady and level at 80m/s, 900m altitude and can drop one bomb
Targets: Two located at (range,elevation) of (700m,100m) and (900,100m)

Diagram Diagram...

Assume no air resistance and that the aircraft flys anyhowSmile .

Using the HP Prime, describe how the aircraft and cannon can be used to hit the two targets at exactly the same time.

Okay, maybe I can nudge things along...

Numerical solution(s) can be obtained for this question using the Solver App and these equations:


where θm is launch angle. I didn't use θ, which is a predefined Home Real var, since I wanted ot use these equations later in CAS...

If you tried using this App, did you run into any issues? Any other solution methods used?

The main issue is the generic syntax error the apps return. I checked the geometry app first and it is so flickery and cumbersome to use that you can barely make use of it.

Then just checked the parabola app, and it is just a gimmick to add an icon.

Finally with the solver, if you entry the expression directly, of course you get the Syntax error that tells you nothing, and the struggle starts changing something, enter, syntax error, changing something, enter, error, etc.

But I still haven't memorized the reserved variable rules so I just try anything. Plus using multiple letter variables converts them to V*A*R. Nice that I don't have to use it for calculus anymore Smile because I really enjoy the programming/graphics side of the device.
Thanks Eric for trying and your feedback.

I agree that the Quadratic and Geometry Apps are not helpful with this type of problem. I also agree that the Solver App is kind of a minefield to get equations into. So far, I found a couple of ways that relate to this problem:

* Create the variables (xt, yt, t, g, v0 etc) in CAS or Home using := or STO first. Then Solver App will let you enter the equations in E1, E2 as xt=v0*t... and yt=-1/2... From here, Num seems to let you solve numerically for variable(s).

** I preferred to first create equations in CAS (eq1, eq2) without first creating the variables. eq1:=xt=v0*COS(θm)*t... Then I assign Solve.E1:=eq1 and same for E2, eq2. Now when I use Solver App (Num view), it prompts me to create the new variables. After saying yes, it allows for numerical solving.

I prefer the second method as it seems to allow for other CAS work, like numeric fsolve() and algebraic solve().
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