Question

Suppose you hit a fly ball with an initial upward velocity of 20 feet per second. Which of the following equations would be a realistic model for the height of the ball after t seconds?

Answer 1

$\bf \qquad \textit{initial velocity}\\\\\begin{array}{llll}\qquad \textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \\\\ \end{array} \quad \begin{cases} v_o=\textit{initial velocity of the object}\\ h_o=\textit{initial height of the object}\\ h=\textit{height of the object at "t" seconds} \end{cases}\\\\ -------------------------------\\\\ \textit{"initial upward velocity of 20 feet per second" simply means } v_o=20$

Answer 2

A=g≈-32

v=⌠a dt  since a≈-32

v=-32t+C, where C is the initial velocity, which we are told is 20 ft/s

v=-32t+20

h=⌠v dt

h=-32t^2/2+20t+C, where C is the initial height, so what is a reasonable initial height?  How about 3 ft since we are swinging a bat around maybe our waist level... maybe :P

h=-16t^2+20t+3

Your choices may have made a different assumption about the initial height of course but you did not show your choices, but certainly it will be:

h(t)=-16t^2+20t+hi, where hi is the initial height in feet.

This of course ignores air resistance and flight dynamics of a spinning ball with seams, which will make a significant difference in real life :)