How Do You Calculate the Combined Momentum of Two Joggers?

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SUMMARY

The combined momentum of two joggers can be calculated using vector components. The first jogger, weighing 81.8 kg and moving east at 1.81 m/s, contributes a momentum of 148.46 kg·m/s in the x-direction. The second jogger, weighing 54.4 kg and moving at 3.00 m/s at an angle of 32.2° north of east, requires decomposition into x and y components, yielding a momentum of 163.20 kg·m/s in the x-direction and 54.78 kg·m/s in the y-direction. The total momentum is found by summing these components, resulting in a magnitude of approximately 215.34 kg·m/s.

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  • Knowledge of vector decomposition in physics
  • Familiarity with trigonometric functions for angle calculations
  • Basic algebra for summing components
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Homework Statement


An 81.8 kg jogger is heading due east at a speed of 1.81 m/s. A 54.4 kg jogger is heading 32.2° north of east at a speed of 3.00 m/s. Calculate the magnitude of the sum of the momenta of the two joggers.


Homework Equations


m1v1 + m2v2 = m1v1' + m2v2'


The Attempt at a Solution


Since they want the sum of the momenta I figured it meant that I would just add up the masses and the velocities as follows:

(81.8)(1.81) + (54.4)(3.00)

However, that was not the correct answer. Also the angle is throwing me off a bit as I don't see how it could fit into this problem. Any help will be greatly appreciated. Thanks.


CaptFormal
 
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Draw a diagram
Remember the momentum in Y (north-south) and X (east-west) is conserved.
 

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