Question 424391
a ball is thrown, its height in feet h after t seconds is given:
h = vt - 16t^2
v=initial upward velocity in feet per second.
:
 if v=21 feet per second, find all values of t which h=6 feet.
 Do not round intermediate steps, round answer 2 decimals.
:
 21t - 16t^2 = 6
A quadratic equation
-16t^2 + 21t - 6 = 0
Use the quadratic formula to find t
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this equation; x=t; a=-16; b=21 c=-6
{{{t = (-21 +- sqrt(21^2-4*-16*-6 ))/(2*-16) }}}
:
{{{t = (-21 +- sqrt(441-384 ))/(-32) }}}
:
{{{t = (-21 +- sqrt(57 ))/(-32) }}}
Two solutions
{{{t = (-21 + 7.5498)/(-32) }}}
t = {{{(-13.450)/(-32)}}}
t = .42 sec, 6 ft on the way up
and
{{{t = (-21 - 7.5498)/(-32) }}}
t = {{{(-28.5498)/(-32)}}}
t = .89 sec, 6ft on the way down
:
:
Looks like this:
{{{ graph( 300, 200, -1, 3, -4, 10, -16x^2+21x, 6) }}}