$\"\"$

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An object of mass $\"\"$ is dropped from a height and the air resistance is proportional to the objects velocity is $\"\"$ , where $\"\"$ is a gravitational constant and $\"\"$ is a proportional constant.

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The solution of differential equation $\"\"$ is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Observe the graph :

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The value of $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The limiting value of the velocity function $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The limiting value of the velocity function is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The limiting value of the velocity function is $\"\"$ .