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Ryder plans to launch a toy rocket in his back yard. He wants to find the formula for the maximum height the rocket can reach without worrying about air resistance. He is given the following two formulas:

$$y=\cfrac { -16 }{ { v }_{ 0 }^{ 2 }\cos ^{ 2 }{ \theta } } { x }^{ 2 }+\left( \tan { \theta } \right) x+{ h }_{ 0 }$$

$$x=\cfrac { 1 }{ 32 } { v }_{ 0 }^{ 2 }\sin { \theta } $$

In the formulas, $x$ is the horizontal distance in feet, $y$ is the vertical distance in feet, ${ h }_{ 0 }$ is the initial height in feet, ${ v }_{ 0 }$ is the initial velocity in feet per second and $\theta $ is the angle measure in degrees. Also, ${ h }_{ 0 }=0$ because Ryder plans to launch his rocket from ground level.

Find the formula for the maximum height the rocket can reach. Then find the maximum height when $\theta =90^\circ$ and ${ v }_{ 0 }=50$.

A

$x=\left( \cfrac { 1 }{ 32 } { v }_{ 0 }^{ 2 }\sin { \theta \cos { \theta } } \right) $
$y\approx 39.1\text{feet}$

B

$x=\left( \cfrac { 1 }{ 32 } { v }_{ 0 }^{ 2 }\sin { \theta \cos { \theta } } \right) $

C

$y\approx 39.1\text{feet}$

D

$x=\left( \cfrac { 1 }{ 32 } { v }_{ 0 }^{ 2 }\sin { \theta \cos { \theta } } \right) $
$y\approx 31.2\text{feet}$

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