Question

a ball is thrown from an initial height of 7 feet with an initial upward - velocity of 28 ft/s. the balls height h (in feet) after t seconds is given by the following.
h = 7 + 28t−16t²
find all values of t for which the balls height is 15 feet.
round your answer(s) to the nearest hundredth.
(if there is more than one answer, use the \or\ button.)

Explanation:

Step1: Set up the equation

Set $h = 15$ in the equation $h=7 + 28t-16t^{2}$, so we get $15=7 + 28t-16t^{2}$.

Step2: Rearrange to standard quadratic form

Rearrange the equation to $16t^{2}-28t + 8=0$. Divide through by 4 to simplify: $4t^{2}-7t + 2=0$.

Step3: Use the quadratic formula

The quadratic formula for $ax^{2}+bx + c = 0$ is $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here $a = 4$, $b=-7$, $c = 2$. First, calculate the discriminant $\Delta=b^{2}-4ac=(-7)^{2}-4\times4\times2=49 - 32 = 17$.

Step4: Find the values of t

$t=\frac{7\pm\sqrt{17}}{8}$.
$t_1=\frac{7+\sqrt{17}}{8}\approx\frac{7 + 4.123}{8}=\frac{11.123}{8}\approx1.39$
$t_2=\frac{7-\sqrt{17}}{8}\approx\frac{7 - 4.123}{8}=\frac{2.877}{8}\approx0.36$

Answer:

$t\approx0.36$ or $t\approx1.39$