Question 89492
The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 90t + 3.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth, and explain which solution is the correct one.
:
When the object strikes the ground, h = 0, so we have:
-16t^2 + 90t + 3 = 0
:
A quadratic equation, that requires the quadratic formula to solve:
a = -16, b = 90, c = 3
:
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{t = (-90 +- sqrt( 90^2 - 4 * -16 * 3 ))/(2*-16) }}}
:
{{{t = (-90 +- sqrt( 8100 - (-192) ))/(-32) }}}
:
{{{t = (-90 +- sqrt( 8100 + 192 ))/(-32) }}}; minus a minus is a plus
:
{{{t = (-90 +- sqrt( 8292 ))/(-32) }}}
:
Do the math here and you should get two solutions:
t = 5.658
and
t = -.033
:
Obviously, it cannot be a neg value when you are dealing with time of an event