You are not logged in.
Pages: 1
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.
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.
Offline
Pages: 1