Solve Applied Problems Involving Vectors
-The magnitude and direction of two forces acting on an object are 35 pounds, $\mathrm { N } 45 ^ { \circ } \mathrm { E }$, and 55 pounds, $\mathrm { S } 30 ^ { \circ } \mathrm { E }$, respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force.
A) $\mid \mathbf { F } \| = 57.04 ; \quad \theta = - 23.6 ^ { \circ }$
B) $\| \mathbf { F } \| = 65.19 ; \theta = - 7.5 ^ { \circ }$
C) $\mid \mathbf { F } \| = 43.30 ; \theta = 2.7 ^ { \circ }$
D) $| \mathbf { F } | = 49.17 ; \theta = - 11.3 ^ { \circ }$

Question

Quizplus · Accepted Answer

To find the resultant force, we decompose the given forces into their x (east-west) and y (north-south) components and then sum these components. For the first force (35 pounds, N 45° E), its components are $35\cos(45^\circ)$ east and $35\sin(45^\circ)$ north. For the second force (55 pounds, S 30° E), its components are $55\cos(30^\circ)$ east and $-55\sin(30^\circ)$ south (negative because it's south). Summing the x-components and y-components gives the resultant force's components. The magnitude of the resultant force is found using the Pythagorean theorem, and the direction angle is found using the arctan of the y-component over the x-component. Calculating these gives a magnitude of 57.04 pounds and a direction angle of -23.6°, indicating the direction is south of east.

Solve Applied Problems Involving Vectors -The Magnitude and Direction of Two

Solve Applied Problems Involving Vectors
-The Magnitude and Direction of Two