24-Ruby IV

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New ode problem

Forum|Forum|13 years ago
September 18, 2012
4 replies
4422 views

New ode problem (for Alan, Viktor and all):

A steel ball (with d=100 mm and Ro=7800 kg/m^3) was thrown upward. He has reached a certain maximum height (h.max=250 m) and fell to the ground after a certain time (t.end=17s).
What is the initial speed of the ball and what is a value of the coefficient of drag k (F.drag=k S Ro.air v^2). Ro.air=1.225 kg/m^3 or is a function of the height.

See for the start here http://communities.ptc.com/message/187832

Calculus_Derivatives

Best answer by ValeryOchkov

Thanks, Alan!

I would like to use the Maximize function but:

PS

Better to have:

V

ViktorKorobov

1-Visitor

Please, Valery. Sorry, without units (MC 14).

Viktor

V

ValeryOchkov

Author

24-Ruby IV

Thanks and Sorry,

not v(t)^2 but v(t)*|v(t)| or v(t)^2*sign(v(t))

And attach please the file!

A

AlanStevens

19-Tanzanite

What is it with you and throwing balls in the air Valery!!!

Oh well, attached is my version - in Prime 2, with units.

Alan

1_AnotherValeryBall-mcdx.zip

V

ViktorKorobov

1-Visitor

Alan, show a picture please. I do not have MC Prime now!

Viktor

V

ValeryOchkov

Author

24-Ruby IV

1) How to do it automatically (see the picture, Mathcad 15 and Mathcad Prime files)?

2) Has the problem solution by this initial data?

19-Tanzanite

Here's my automatic answer. Of course the up and down movements are not symmetrical, as I had assumed in my first post, because of the drag! I've not bothered with the Archimedes upthrust as it's a small effect.

Alan

Here are the images, for Viktor: