Question 328191
an object is propelled upward from a height of 96ft at an initial velocity of 80ft per second,
its height after t seconds is given by the equation h = -16t^2 + 80t + 96 where h is in feet.
 After how many seconds will the object reach a height of 196ft?
:
-16t^2 + 80t + 96 = h
Replace h with 196
-16t^2 + 80t + 96 = 196
-16t^2 + 80t + 96 - 196 = 0
-16t^2 + 80t - 100 = 0
Simplify & change the signs, divide by -4, (easier to factor)
4t^2 - 20x + 25 = 0
Factors to
(2t-5)(2t-5) = 0
2t = 5
t = {{{5/2}}}
t = 2.5 seconds it will be 196 ft (this is also the max height)
:
Graphically; t on the x axis, h on the y axis
{{{ graph( 300, 200, -4, 8, -100, 240, -16x^2+80x+96) }}}