How Do You Calculate the Combined Momentum of Two Joggers?

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To calculate the combined momentum of two joggers, one must consider both their masses and velocities in vector form. The first jogger weighs 81.8 kg and moves east at 1.81 m/s, while the second jogger weighs 54.4 kg and moves at a 32.2° angle north of east at 3.00 m/s. The correct approach involves breaking down the second jogger's momentum into its x (east) and y (north) components before summing them with the first jogger's momentum. The initial attempt to simply add the products of mass and velocity was incorrect due to the need to account for directional components. Understanding the conservation of momentum in both the x and y directions is crucial for solving this problem accurately.
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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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