What Is the Magnitude of the Pulling Force Exerted by the Wife?

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The discussion focuses on calculating the magnitude of the pulling force exerted by the wife while pulling a wagon. Given that both parents do the same amount of work over the same distance, the equations for work done by each are set equal to each other. The husband's pulling force is 66 N at an angle of 58° above the horizontal, while the wife's force is at 34°. By equating the work done, the relationship simplifies to 66 * cos(58) = FORCE * cos(34), allowing for the calculation of the wife's pulling force. The final formula derived is 66 * cos(58)/cos(34) to find her force.
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Homework Statement



A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force and pulls the wagon through the same displacement. They do the same amount of work, but the husband's pulling force is directed 58° above the horizontal, while the wife's pulling force is directed 34° above the horizontal. The husband pills with a force whose magnitude is 66 N. What is the magnitude of the pulling force exerted by his wife?


Homework Equations





The Attempt at a Solution

 
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Any ideas on how to do this before we help?
 
w = f * d (vectors)

w of man = 66 * cos(58) * D

w of woman = force * cos(34) * D

w of woman = w of man

66 * cos(58) * D = FORCE * cos(34) * D

the distances cancel out and you are left with

66 * cos(58)/cos(34) = answer
 

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