Solve the problem.
-A force of $90 \mathrm { lb }$ acts on an object at an angle of $55 ^ { \circ }$. A second force of $100 \mathrm { lb }$ acts on the object at an angle of $- 60 ^ { \circ }$. Find the direction and magnitude of the resultant force.
A) $| \mathrm { F } | = 98.92 \mathrm { lb } , \theta = - 4.2 ^ { \circ }$
B) $| \mathrm { F } | \approx 102.43 \mathrm { lb } , \theta \approx - 7.2 ^ { \circ }$
C) $| \mathrm { F } | = 101.47 \mathrm { lb } , \theta \approx 7.2 ^ { \circ }$
D) $| \mathrm { F } | \approx 1.43 \mathrm { lb } , \theta = - 2 ^ { \circ }$

Question

Quizplus · Accepted Answer

To find the resultant force, we break each force into its horizontal (x) and vertical (y) components and then sum these components. For the first force (90 lb at 55 degrees): $F_{1x} = 90\cos(55^\circ)$, $F_{1y} = 90\sin(55^\circ)$. For the second force (100 lb at -60 degrees): $F_{2x} = 100\cos(-60^\circ)$, $F_{2y} = 100\sin(-60^\circ)$. Summing the x and y components gives the total x and y components of the resultant force, from which we can calculate its magnitude and direction using Pythagoras' theorem and trigonometry. The calculations align with option B, indicating it as the correct answer.

Solve the Problem 90lb90 \mathrm { lb }90lb Acts on an Object at an Angle Of

Solve the Problem $90 \mathrm { lb }$ Acts on an Object at an Angle Of