Question 162802
Suppose Charlie O’Brian of the braves hits a baseball straight upward at 150 ft/sec from a height of 5 ft. Use the formula to determine how long it takes the ball to return to the earth. 
:
Let t = time in seconds
:
The formula has 3 parts, 
gravity, -16t^2; negative because it pulls downward
upward velocity, 150t positive because it's going upward
initial height, 5 ft; it starts from 5 ft above the ground
:
The formula
h = -16t^2 + 150t + 5
:
When it returns to earth h = 0, therefore:
-16t^2 + 150t + 5 = 0
:
We have to use the quadratic formula to solve for t:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this problem: a=-16; b=150; c=5
{{{t = (-150 +- sqrt(150^2 - 4*-16*5 ))/(2*-16) }}}
:
{{{t = (-150 +- sqrt(22500 + 320 ))/(-32) }}}
:
{{{t = (-150 +- sqrt(22820))/(-32) }}}
:
We want the positive solution here:
{{{t = (-150 - 151)/(-32) }}}
t = {{{(-301)/(-32)}}}
t = + 9.4 sec to return to earth