My pre-cal teacher has been working on parametric equations with us recently and I am quite confused on the subject.
I understand that parametric equations, unlike standard functions, apply a parameter, most often t for time. And, one gives t as input, and receives output from x and y. Not sure if this is always the case, but it has been what I've seen most often.
I checked out the wikipedia article on parametric equations and the kinds of problems I usually have problems with are the ones explained at the top, "A simple kinematical example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion."
OK, so I have the following problem:
An NFL punter at the 15-yard line kicks a football with an initial velocity of 95 feet per second at an angle of elevation of 18°. Let t be the elapsed time since the football is kicked.
a) Write the parametric equations of this problem.
b) With t = 0 at the time of the kick, how many seconds is the ball in the air?
c) Where does the ball land given the kick is straight and from the 15 yard line?
So, my biggest problem is finding the parametric equations described in part a. Once I have that figured out, I should be able to do parts b and c.
Now, should I create a non-parametric model first, and then parametricize that model?
Or, should I start with a parametric model from scratch?
Also, do I need to know some information other than what is given?
We are given:
Starting Position: 45-foot line
Initial Velocity: 95 feet/second (isn't there a formula describing this as v not?)
Angle of Elevation: 18°
Any help is appreciated!