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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.

1 Answer

6 votes

Answer:

t=0.64s and t=1.17s

Step-by-step 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=(-b\pm√(b^2-4ac) )/(2a)

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


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

Therefore, we have:


\begin{gathered} t=\frac{-29+\sqrt[]{73}}{-32}\text{ or }t=\frac{-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.

User Ed Barbu
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