Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force
(a)
Minimum speed to reach the opposite side.
Answer to Problem 81P
The speed is
Explanation of Solution
This system has to be solved using spherical polar coordinates with
Considering the geometry, write the equation to determine
Here
Write the equation for energy conservation of the system
Here
Write the equation for initial and final kinetic energy.
Here
Write the expression for gravitational potential energy at A, B and C.
Here
Write down the equation for change in internal energy.
Here
Substitute (III), (IV) and (V) in (II)
Rearrange (VI) in terms of
Conclusion:
Substitute
Substitute
The speed is
(b)
Minimum speed for combined swing.
Answer to Problem 81P
The speed is
Explanation of Solution
Write down the equation for energy conservation
Here
Write down the equation for mechanical energy
Here
Substitute (III), (IV) and (IX) in (VIII)
Here
Rearrange (X) in terms of
Conclusion:
Substitute
The speed is
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Chapter 7 Solutions
Principles of Physics: A Calculus-Based Text
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