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Answer :
Final answer:
The magnitude of the sum of the momenta of the two joggers is 252.8 kg.m/s, and the direction is 24.3° north of east.
Explanation:
The sum of the momenta of the two joggers can be found using the principles of vector addition. Firstly, let's calculate the momentum of each jogger: Momentum (p) = mass (m) × velocity (v). Therefore, the momentum of the first jogger (p1) is 84 kg × 1.5 m/s = 126 kg.m/s, and all of it is in the due east direction. The momentum of the second jogger (p2) has both an east and a north component due to its angle from east. The east component = 75 kg × 2.4 m/s × cos(48°) = 112.6 kg.m/s. The north component = 75 kg × 2.4 m/s × sin(48°) = 106.6 kg.m/s. Then, we add the east components of p1 and p2 and the north component of p2 together to get the net momentum of the joggers. The resultant east momentum = 126 kg.m/s + 112.6 kg.m/s = 238.6 kg.m/s (east), and the resultant north momentum = 106.6 kg.m/s (north). (a) The magnitude of the sum of their momenta is √{[238.6 kg.m/s]² + [106.6 kg.m/s]²}= 252.8 kg.m/s. (b) To find the direction of the sum of the momenta, take the arctan of the north component over the east component. This gives us the angle the resultant momentum vector makes with respect to the horizontal. Therefore, the direction is arctan(106.6/238.6) = 24.3° north of east.
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