Math Is Fun Forum

Luke Harusame

Guest

Help with parametrics

Hey, everybody.  I'm about to take a test tomorrow, and there's just one concept that I can't quite get.  Whenever the teacher does it I can follow, but then when I try and do it myself I freeze up and I can't remember a thing.  Could you shed some light on this?

"Many people enjoy the game of darts. To play darts, you stand 8 feet from a dart board and throw three darts per round, seeking points totaling 500

Suppose you are most accurate when you throw a dart at a 20 degree angle to the horizontal. If the bull's-eye is at the same height as your release point, about what initial velocity must you impart to the dart to hit the bull's-eye?"

To start these problems I like to put all the relevant data into a way I can understand. In this case, it's the parametric equation.

x = Atcos(20)-8

y = Atsin(20)

I assumed that 8 feet away means -8, but really it could be either as long as you keep things consistent.

If A equals the initial velocity of the dart, then how the hell do I solve for it?

Any help is greatly appreciated.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Help with parametrics

you're forgetting about gravity.
Atcos(20) = 8 (moves 8 feet horizontally)
Atsin(20) - ½gt² = 0 (returns to intial height)

since you're working in feet, A and g must be feet per second, and feet per second squared respectively, otherwise you can convert the 8feet into metres, and then use standard units of m/s and m/s²

g is acceleration due to gravity, supposing its not given anywhere on the question or paper at all, take g = 9.81m/s² (correct to 3sf) = 32.2feet/s² (3sf)

Atcos(20) = 8
Atsin(20) - ½gt² = 0 (returns to intial height)

substitute first equation into second:

Last edited by luca-deltodesco (2007-10-08 18:45:32)

---

The Beginning Of All Things To End.
The End Of All Things To Come.