Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum
 It is currently Mon Mar 10, 2014 6:16 pm

 All times are UTC - 5 hours

 Page 1 of 1 [ 4 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Firing Arrows in a Cartesian PlanePosted: Sun Jan 26, 2014 4:05 pm

Joined: Thu Jun 03, 2010 2:25 pm
Location: Farmington, NM
Before I pose the question i have, let me give a bit of backstory:

I've been working on a video game project recently, and one of the bits of code I had to write was to set initial movement vectors to an object so it would follow a ballistic trajectory and go through a specified point. There were three circumstances I had to code for: a constant maximum height so the direction and magnitude of the vector had to be determined, a constant direction so the magnitude of the vector had to be determined, and a constant magnitude so the direction had to be determined. The first two cases were not very interesting, but the last case brought about an interesting problem. There are areas of the grid that a fired projectile obviously cannot hit, and areas that it can. What I was interested in was where those areas actually are.

If a projectile is fired along a ballistic trajectory with a predetermined speed and gravity on a cartesian graph, what is the equation of the line that defines where the projectile cannot possibly reach?

I think it's a conic section, although I have no way to be sure. Does anyone know how to solve this?

_________________
Autism Speaks can go away. I have Autism. I can speak for myself.

"You say tomater, I zader matermorts." - Coach Z

Top

 Post subject: Re: Firing Arrows in a Cartesian PlanePosted: Thu Feb 06, 2014 2:15 am

Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
It's a parabola, called the parabola of safety. The French wiki page has more explanation, including the final equation y = h - x^2/4h.
This gives y(2h)=0, showing that a projectile can reach twice as far horizontally than it can reach when fired straight up.

_________________
Jaap

Jaap's Puzzle Page:
http://www.jaapsch.net/puzzles/

Top

 Post subject: Re: Firing Arrows in a Cartesian PlanePosted: Thu Feb 06, 2014 12:53 pm

Joined: Thu Jun 03, 2010 2:25 pm
Location: Farmington, NM
Thank you for the link, Jaap. That article was very helpful despite the fact that I don't speak French. But now I have another (slightly more relevant) question: What are the equation(s) of the parabola(s) that pass through an arbitrary point within the "parabola of safety?" I think I can figure out how to determine the initial angle from that equation.

_________________
Autism Speaks can go away. I have Autism. I can speak for myself.

"You say tomater, I zader matermorts." - Coach Z

Top

 Post subject: Re: Firing Arrows in a Cartesian PlanePosted: Thu Feb 06, 2014 1:14 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Jorbs3210 wrote:
Thank you for the link, Jaap. That article was very helpful despite the fact that I don't speak French. But now I have another (slightly more relevant) question: What are the equation(s) of the parabola(s) that pass through an arbitrary point within the "parabola of safety?" I think I can figure out how to determine the initial angle from that equation.

Check out the graph that shows the line OC passing through the focus of the parabola. It should be easy to compute the parabola by first computing the location of the focus (the point the horizontally fired object (blue curve) crosses the OC line) and then from the focus and points O and C computing the resulting parabola.

_________________
Prior to using my real name I posted under the account named bmenrigh.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 4 posts ]

 All times are UTC - 5 hours

#### Who is online

Users browsing this forum: katsmom and 2 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ Announcements General Puzzle Topics New Puzzles Puzzle Building and Modding Puzzle Collecting Solving Puzzles Marketplace Non-Twisty Puzzles Site Comments, Suggestions & Questions Content Moderators Off Topic

Forum powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group