Question 124223
The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
:
When it hits the ground h = 0, therefore:
:
-16t^2 + 30t + 3 = 0
:
Using the quadratic formula:
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this problem; a=-16, b=30, c=3
{{{t = (-30 +- sqrt(30^2 - 4 *-16 * 3 ))/(2*-16) }}}
:
{{{t = (-30 +- sqrt(900 -(-192) ))/(-32) }}}
: 
{{{t = (-30 +- sqrt(900 + 192 ))/(-32) }}}
: 
{{{t = (-30 +- sqrt(1092))/(-32) }}}
:
Two solutions:
{{{t = (-30 + 33.0454)/(-32)}}}
:
{{{t = (3.0454)/(-32)}}}
:
t = -.095; not a solution
and
{{{t = (-30 - 33.0454)/(-32)}}}
:
{{{t = (-63.0454)/(-32)}}}
:
t = +1.970 seconds to hit the ground
:
:
You can substitute this value for t in the original equation and confirm
that it does, in fact, = 0, or very close to it