An athlete runs 142.0 m in a direction 28° North of East and then 105.0 m in a direction 40° East of North. Using the components, determine the resultant displacement.

Sa madaling salita, ang kolonyalismo ay isang anyo ng imperyalismo.

Answered by johnvincentalejandro | 2024-10-16

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Answered by faijanur2023 | 2024-10-16

[tex]\text{Given:} \\[/tex][tex]D_1 = 142.0 \, \text{m}, 28^\circ \text{ N of E} \\[/tex][tex]D_2 = 105.0 \, \text{m}, 40^\circ \text{ E of N} \\[/tex][tex]\text{Find:} \\[/tex][tex]\text{Resultant displacement (R) and direction (}\theta\text{)} \\[/tex][tex]\text{Solution:} \\[/tex][tex]D_{1x} = 142.0 \cos(28^\circ) \approx 125.32 \, \text{m} \\[/tex][tex]D_{1y} = 142.0 \sin(28^\circ) \approx 66.77 \, \text{m} \\[/tex][tex]D_{2x} = 105.0 \sin(40^\circ) \approx 67.51 \, \text{m} \\[/tex][tex]D_{2y} = 105.0 \cos(40^\circ) \approx 80.34 \, \text{m} \\[/tex][tex]R_x = D_{1x} + D_{2x} \approx 192.83 \, \text{m} \\[/tex][tex]R_y = D_{1y} + D_{2y} \approx 147.11 \, \text{m} \\[/tex][tex]R = \sqrt{R_x^2 + R_y^2} \approx 242.54 \, \text{m} \\[/tex][tex]\theta = \arctan\left(\frac{R_y}{R_x}\right) \approx 37.36^\circ \text{ N of E} \\[/tex][tex]\text{Answer:} \\[/tex][tex]\text{Resultant displacement } R \approx 242.54 \, \text{m} \\[/tex][tex]\text{Direction } \theta \approx 37.36^\circ \text{ N of E}[/tex]

Answered by GreatBlueSpot | 2025-02-09