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")
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:
Rearranging to make it simpler to put into a quadratic form: [tex]0 = -16t^2+23t-8[/tex]
Now, let's plug it into the quadratic equation: [tex] \frac{-23+ \sqrt{(23)^2-4(-16)(-8)} }{2(-16)} [/tex] and [tex]\frac{-23- \sqrt{(23)^2-4(-16)(-8)} }{2(-16)}[/tex]
Solving the quadratic gives us: 0.5899 and 0.8476
So, your answer is: h = 14 when t = 0.5899 or t = 0.8476
