Concept explainers
(a)
The magnitude of the velocity of the parasailer as a function of time.
Answer to Problem 11.164P
Explanation of Solution
Given information:
Length of rope is defined as,
Constant velocity of the boat is
The angle is increasing at
The velocity in radial and transverse components,
The acceleration in radial and transverse components,
Calculation:
According to given information,
Convert,
We know that,
Therefore,
According to the explanation, the relative velocity of parasailer with respect to boat is,
The relative co-ordinates of the relative velocity is equal to,
Therefore the velocity of parasailer is equal to,
We can rewrite this as,
Where,
To find the magnitude,
Now, plot the graph,
Conclusion:
The magnitude of velocity of the parasailer is equal to,
The relevant graph is shown above.
(b)
The magnitude of acceleration of parasailer at
Answer to Problem 11.164P
Explanation of Solution
Given information:
Length of rope is defined as,
Constant velocity of the boat is
The angle is increasing at
The velocity in radial and transverse components,
The acceleration in radial and transverse components,
Calculation:
According to given information,
Convert,
We know that,
Therefore,
According to the explanation, the relative acceleration of parasailer with respect to boat is,
The acceleration of parasailer is equal to,
At,
Therefore the magnitude is equal to,
Conclusion:
The magnitude of acceleration of the parasailer is equal to,
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Chapter 11 Solutions
Vector Mechanics For Engineers
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