$\"\"$

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The acceleration due to gravity is $\"\"$ ft/sec/sec.

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The initial velocity of ball is $\"\"$ ft/s.

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$\"\"$ ft/sec.

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The initial height when ball is thrown up is $\"\"$ feet.

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$\"\"$ ft.

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Acceleration of a ball is rate of change in velocity $\"\"$ .

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Velocity is $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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The position of a ball at time $\"\"$ is $\"\"$ .

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Velocity of a ball is rate of change in position $\"\"$ .

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Position at time $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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$\"\"$

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The ball reaches maximum height when velocity is zero.

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$\"\"$

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The ball reaches maximum height when time $\"\"$ sec.

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The position of ball when time $\"\"$ sec is,

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$\"\"$

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The maximum height of ball is $\"\"$ ft.

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$\"\"$

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The maximum height of ball is $\"\"$ ft.