$\"\"$

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(a)

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Position function of a object moving downwards is $\"\"$ .

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As the object is falling down then $\"\"$ .

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where $\"\"$ is the initial height.

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$\"\"$ is the initial velocity.

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$\"\"$ is the acceleration due to gravity.

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Position Function $\"\"$ .

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$\"\"$ .

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Therefore, the position vector is $\"\"$ .

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$\"\"$

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When the object reaches the ground level then $\"\"$ .

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$\"\"$

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Therefore, at time $\"\"$ sec, the object will reach the ground.

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$\"\"$

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(b)

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Angle of elevation is $\"\"$ .

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$\"\"$

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Apply derivative with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Rate of change in angle of elevation at $\"\"$ is

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$\"\"$

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Rate of change in angle of elevation at $\"\"$ is $\"\"$ .

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Rate of change in angle of elevation at $\"\"$ is

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$\"\"$

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Rate of change in angle of elevation at $\"\"$ is $\"\"$ .

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$\"\"$

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(a) The position vector is $\"\"$ .

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The object will reach the ground at $\"\"$ .

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(b)

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Rate of change in angle of elevation at $\"\"$ is $\"\"$ .

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Rate of change in angle of elevation at $\"\"$ is $\"\"$ .