$\"\"$

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

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

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$\"\"$ .

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

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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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The position of a balloon 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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The height of balloon is $\"\"$ feet.

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

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$\"\"$ .

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

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$\"\"$ .

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The balloon reaches ground when height is zero.

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

\

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$\"\"$

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$\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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$\"\"$ is not consider, the time can not be negative.

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$\"\"$ .

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The balloon reaches ground when time $\"\"$ sec.

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$\"\"$

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(b)

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$\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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The balloon reaches the ground when $\"\"$ sec.

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$\"\"$

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$\"\"$

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The velocity is $\"\"$ ft/sec. $\"\"$

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(a) The balloon reaches ground when time $\"\"$ sec.

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(b)The velocity is $\"\"$ ft/sec.