Concept explainers
(a)
To show:The speed of a sky diver, whose acceleration is given by the equation
(a)
Explanation of Solution
Given:
The equation for the acceleration
The expressions for the terminal speed
The speed of the sky diver at time
Calculation:
Rewrite equation (1) using the expression for acceleration
Rearrange the above equation as follows:
Integrate both sides of the equation.
Therefore,
Evaluate the integral
Let
Therefore,
Rewrite equation (5) as shown:
The expression
Therefore, equation (7) takes the form,
Use the identity,
Hence write equation (8) as,
Therefore, equation (4) can be written as ,
Substitute the value of
Apply the initial conditions of the sky diver
Therefore, equation (10) can be written as,
Therefore,
From equations (2)
Therefore, equation (12) can be written as,
Hence,
Conclusion:
Thus, it is proved that the speed of a sky diver, whose acceleration is given by the equation
(b)
To Find:The fraction of the terminal speed is the speed of the sky diver at time
(b)
Answer to Problem 119P
At time
Explanation of Solution
Given:
The equation for the speed of the sky diver
Calculation:
Substitute
Conclusion:
Thus, at time
(c)
To graph:
(c)
Explanation of Solution
Given:
The equation for the speed of the sky diver
Calculation:
In a spread sheet, calculate the values of
Conclusion:
Thus, it can be seen from the graph that the sky diver attains the terminal velocity at around 20 s.
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Chapter 2 Solutions
Physics for Scientists and Engineers
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