Question

a ball is thrown from an initial 5 feet with an initial upward 29 ft per second in the balls height H in feet after T seconds is given by the followingh=5+29t-16t^2find all the values of t for which the balls height is 17 ft round all your answers tk the nearest hundredth.

Answer 1

Answer:

t=0.64s and t=1.17s

Explanation:

The function that models the height of the ball is given below:

$h(t)=5+29t-16t^2$

When the ball's height is 17 feet, we have:

$\begin{gathered} 17=5+29t-16t^2 \\ 0=-17+5+29t-16t^2 \\ -16t^2+29t-12=0 \end{gathered}$

We solve the quadratic equation derived above for the values of t.

We use the quadratic formula.

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

In our own equation: a=-16, b=29, c=-12

$\begin{gathered} t=\dfrac{-29\pm\sqrt[]{29^2-4(-16)(-12)}}{2(-16)} \\ =\dfrac{-29\pm\sqrt[]{841-768}}{-32} \\ =\dfrac{-29\pm\sqrt[]{73}}{-32} \end{gathered}$

Therefore, we have:

$\begin{gathered} t=\dfrac{-29+\sqrt[]{73}}{-32}\text{ or }t=\dfrac{-29-\sqrt[]{73}}{-32} \\ t=0.6392\text{ or t=1}.1733 \\ t=0.64\text{ or t=1}.17\text{ (to the nearest hundredth)} \end{gathered}$

The values of t for which the ball's height is 17 ft are 0.64 seconds and 1.17 seconds.