http://www.ck12.org Chapter 10. Polar and Parametric Equations
You might observe that the two graphs overlap at about 125 feet, but this is unimportant because they are probably
at that location at different times. Plot the distance over time and see how close the footballs actually get in midair.
x 3 =t
y 3 =√
(x 2 −x 1 )^2 +(y 2 −y 1 )^2The TI-83 may run slower than the TI-84 when you do this calculation depending on how small yourTste pis. The
resulting graph is not a parabola and the calculator cannot find a minimum in the way it can in other circum-
stances. Still, you can trace and determine that the footballs get 5.36 feet or closer in midair.
- Don’t let the 10 second difference confuse you. In order to deal with the time difference, use(t+^16 )instead oft
in each equation. Whent=0, ten seconds(^16 of a minute)have already elapsed.
x=− 48 ·sin(π
2(
t+^16))
y=− 48 ·cos(π
2(
t+^16))
+ 50
Att= 3 ,x≈ 46 .36 andy≈ 37. 58