Answer:
Fx= 50.0 Pounds : Components of the force along the x-axis
Fy= 86.6 Pounds : Component of the force along the y-axis
Step-by-step explanation:
Conceptual Analysis
To find the components (Fx, Fy) of the total force (F), we apply the trigonometric concepts for a right triangle, where the perpendicular sides of the triangle are the components (Fx, Fy) of the force (F), the hypotenuse (h) is the magnitude of the total force F and β is the angle that forms the horizontal component with the hypotenuse.
Formulas
cos β : x/h : x: side adjacent to the β angle h: hypotenuse (1)
sin β = y/h : y: side opposite to the β angle h: hypotenuse (2)
Known Data
Known data
F= 1.00 * 10² pounds = 100 pounds : magnitude of total force
β = 60.0° to the x-axis. : Angle that forms the force with the x-axis
Problem Development
We apply the formula 1 to calculate horizontal component (Fx)
cos β :Fx/F
Fx= F cosβ = 100*cos 60° = 50.0 Pounds
We apply the formula 2 to calculate vertical component (Fy)
sin β = Fy/F
Fy= F sinβ = 100*sin 60° = 86.6 Pounds