Question

A bal is thrown from an initial height of 4 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after seconds is given by the following.Find values of for which the ball's height is 12 feet.Round your answers to the nearest hundredth(If there is more than one answer use the "or" button.)

Answer 1

given the equation,

h = 4 + 23t - 16t^2

given h = 12

12 = 4 + 23t - 16t^2

lets take everything to the left

16t^2 - 23t + 12 - 4

16t^2 - 23t + 8

lets use formular methos to solve the equation

`x\text{ = }-b\text{ }\pm\frac{\sqrt[]{b2\text{ - 4ac}}}{2a}`

let t = x

a = 16

b = 23

c = 8

so,

`\begin{gathered} x\text{ = -(-23) }\pm\sqrt[]{(-23)(-4(16)(8))/(2(16))} \\ =\text{ 23 }\pm\text{ }\sqrt[]{529(-512)/(32)} \\ =\text{ 23 }\pm\sqrt[]{(17)/(32)} \\ \text{therefore,} \\ t=\text{ 23 + }\sqrt[]{\frac{17}{32\text{ }}}\text{ or 23 -}\sqrt[]{(17)/(32)} \end{gathered}`