(a)
The skydiver acceleration when her speed is
(a)
Answer to Problem 28P
The skydiver acceleration when her speed is
Explanation of Solution
When an object passes through the air it experiences drag force due to the air. The drag force is directly proportional to the square of the velocity of the object.
Write the expression for resistive force by the air on the skydiver as.
Here,
The forces act on the skydiver as shown below.
Write the expression corresponding to Newton’s second law of motion in
Here,
Substitute
Simplify the equation (II) for
At the terminal speed of the skydiver, the acceleration becomes zero. If the acceleration is zero then the velocity becomes terminal velocity.
Substitute
Simplify the above expression for
Here,
Conclusion:
Substitute
Substitute
The positive direction of the acceleration indicates downward direction.
Thus, the skydiver acceleration when her speed is
(b)
The drag force on the skydiver when her speed is
(b)
Answer to Problem 28P
The drag force on the skydiver when her speed is
Explanation of Solution
At the terminal speed, the weight of the skydiver becomes equal to the drag force.
Write the expression corresponding to the condition of equilibrium in
Conclusion:
Substitute
The positive sign indicates an upward direction of the force.
Thus, the drag force on the skydiver when her speed is
(c)
The drag force on the skydiver when her speed is
(c)
Answer to Problem 28P
The drag force on the skydiver at a speed of
Explanation of Solution
Conclusion:
Substitute
The positive sign of the resistive force indicates an upward direction of the force.
Thus, the drag force on the skydiver at a speed of
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