Answer :
Answer: [tex]322\ lb[/tex]
Step-by-step explanation:
Given
The magnitude of the force [tex]F=350\ \text{Pounds}[/tex]
The force makes an angle of [tex]67^{\circ}[/tex] with the horizontal
So, the components of the force are
[tex]\Rightarrow F\cos 67^{\circ}, F\sin 67^{\circ}\\\Rightarrow F\cos 67^{\circ}=350\cos 67^{\circ}\\\quad \quad =136.75\ lb\\\text{Similarly, }\\\Rightarrow F\sin 67^{\circ}=350\sin 67^{\circ}\\=322.17\ lb[/tex]
The larger among the two is [tex]F\sin 67^{\circ}[/tex] i.e. [tex]322\ lb[/tex]
The larger component is approximately 322 pounds .
Resolving a Force into Components
To find the larger component of a force of 350 pounds that makes an angle of 67° with the horizontal, we need to resolve this force into its horizontal and vertical components using trigonometric functions.
- Calculate the horizontal component (Fₓ):
Fₓ = F x cos(θ)
Fₓ = 350 x cos(67°)
Fₓ ≈ 350 x 0.3907 ≈ 136.745 pounds - Calculate the vertical component (Fy):
Fy = F x sin(θ)
Fy = 350 x sin(67°)
Fy ≈ 350 x 0.9210 ≈ 322.35 pounds
Since the vertical component is larger, the larger component is approximately 322 pounds.
