Question

A ball is thrown from an initial height of 6 feet with an initial upward velocity of 23ft/s . The ball's height h (in feet) after t seconds is given by the following. h=6+23t-16t^2 Find all values of t for which the ball's height is 14 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, say "or")

Answer 1

There's a lot of extra information here. All you are really concerned with is solving the polynomial for roots. You want t when h = 14. So let's do it:

$14 = 6+23t-16t^2$
$8=23t-16t^2$

Rearranging to make it simpler to put into a quadratic form:
$0 = -16t^2+23t-8$

Now, let's plug it into the quadratic equation:
$\frac{-23+ \sqrt{(23)^2-4(-16)(-8)} }{2(-16)}$
and
$\frac{-23- \sqrt{(23)^2-4(-16)(-8)} }{2(-16)}$

Solving the quadratic gives us:
0.5899 and 0.8476

So, your answer is: h = 14 when t = 0.5899 or t = 0.8476