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(a)
An object is dropped from the height of .
Let the velocity of a object at time be .
Velocity at time is .
Initial velocity is zero.
Acceleration is equal to acceleration of gravity .
Graph :
Graph the initial velocity :
Velocity of the object at time is .
(b)
Velocity of the object at time is .
Velocity of the object is the rate of change in distance .
Integrate on both sides.
At , height then .
Therefore the position function is .
(c)
If air resistance is considered then rate of change in velocity is
Integrate on both sides.
At , Velocity then .
Velocity function is .
(d)
Find .
Substitute in the function.
Therefore .
(e)
Velocity function is .
Integrate the velocity function.
At , height then .
.
Substitute in the velocity function.
.
Graph:
Graph the function and .
Time required for the object to reach the ground.
Time required when air resistance was neglected is .
Therefore additional time taken by air resistance is
Additional time required to reach ground when air resistance is considered is .
(f)
If value is increased then the time taken by the object to reach ground decreases.
Consider .
Time taken by the object to reach ground when air resistance is not considered is .
Time taken by the object to reach ground when air resistance is considered is .
The time taken by the object to reach ground decreases when air resistance is considered.
(a) Velocity of the object at time is .
(b) The position function is .
(c) Velocity function when air resistance is considered is .
(d) .
(e) Additional time taken to reach ground .
(f) The time taken by the object to reach ground decreases when is increased.
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