$\"\"$

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The height is $\"\"$ .

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The angle is $\"\"$ .

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The value of $\"\"$ .

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(a)

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Time as a parameter in parametric equations are $\"\"$ and $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, the parametric equations of the ball as a function of time are $\"\"$ and $\"\"$ , Where $\"\"$ is the velocity at which the ball leaves the bat.

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$\"\"$

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(b)

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Find the time when the ball is in the maximum height.

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The inital speed is $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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The maximum height occurs at the vertex of the quadratic function.

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The maximum height is at $\"\"$ .

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The quadratic equation is $\"\"$ .

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The general form of quadratic equation is $\"\"$ .

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Compare the equation with general form.

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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Substitute $\"\"$ , $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The maximum height occurs at $\"\"$ .

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substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Therefore, the maximum height is occurs at $\"\"$ .

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$\"\"$

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(c)

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How far is the ball from home plate at its maximum height.

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The maximum height occurs is occurs at $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, the ball will reach its maximum height when it is $\"\"$ from home plate.

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$\"\"$

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(d)

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The ball will reach the left field fence when $\"\"$ .

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Equate $\"\"$ to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The ball will take $\"\"$ to reach the left field fence when $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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The left field fence is $\"\"$ , the ball will clear by green monster by $\"\"$ .

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$\"\"$

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(a) The parametric equations are $\"\"$ and $\"\"$ .

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(b) The maximum height is occurs at $\"\"$ .

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(c) The ball will reach its maximum height when it is $\"\"$ from home plate.

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(d) The ball will clear by green monster by $\"\"$ .