Question

a ball is thrown from an initial height of 4 feet with an initial upward velocity of 17 ft/s. the balls height h (in feet) after t seconds is given by the following.
( h = 4 + 17t - 16t^2 )
find all values of t for which the balls height is 8 feet.
round your answer(s) to the nearest hundredth.
(if there is more than one answer, use the \or\ button.)

Explanation:

Step1: Set height h equal to 8

$8 = 4 + 17t - 16t^2$

Step2: Rearrange into standard quadratic form

$16t^2 - 17t + 4 = 0$

Step3: Apply quadratic formula $t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, $a=16$, $b=-17$, $c=4$
$$t=\frac{17\pm\sqrt{(-17)^2-4(16)(4)}}{2(16)}$$

Step4: Calculate discriminant

$\sqrt{289 - 256} = \sqrt{33} \approx 5.7446$

Step5: Solve for two t values

$t_1=\frac{17 + 5.7446}{32} \approx \frac{22.7446}{32} \approx 0.71$
$t_2=\frac{17 - 5.7446}{32} \approx \frac{11.2554}{32} \approx 0.35$

Answer:

$t = 0.35$ seconds or $t = 0.71$ seconds