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Question

A vector A⃗ has a magnitude of 40.0 m and points in a direction 20.0∘ below the positive x axis. A second vector, B⃗ , has a magnitude of 75.0 m and points in a direction 50.0∘ above the positive x axis. Using the component method of vector addition, find the magnitude of the vector. Using the component method of vector addition, find the direction of the vector.

Answer

The magnitude of the vector R⃗ is 94.7 meters and its direction can be expressed as 27.9 degrees above the positive x-axis. To solve this problem using the component method of vector addition, we must break down each vector into its x and y components. The magnitude of vector A⃗ is 40.0 meters and its angle with the positive x-axis is 20.0 degrees below the positive x-axis. Hence, the x and y components of A⃗ can be obtained using trigonometry as Ax = 37.0 meters and Ay = -13.7 meters. For vector B⃗, the magnitude is 75.0 meters and the angle it makes with the positive x-axis is 50.0 degrees above the positive x-axis. Therefore, the x and y components of B⃗ can be found using trigonometry as Bx = 48.2 meters and By = 57.6 meters. To find the resultant vector, we add the x and y components of A⃗ and B⃗, separately. Thus, Rx = 85.2 meters and Ry = 43.9 meters. The magnitude of the resultant vector R⃗ is calculated as |R⃗| = sqrt(Rx^2 + Ry^2) = 94.7 meters. To determine the direction of the resultant vector, we use trigonometry to find the angle that R⃗ makes with the positive x-axis, which is 27.9 degrees. Further insights on the magnitude of vector can be accessed on this link: brainly.com/question/3184914 #SPJ1.