Final answer:
The statement that the vertical component of the force is 17.32 N is false. By using trigonometric functions, we calculate that the vertical component is approximately 69.28 N, given a horizontal component of 40 N at an angle of 60 degrees to the horizontal.
Step-by-step explanation:
If a force is inclined at 60 degrees to the horizontal, and the horizontal component of the force is 40 N, we can calculate the vertical component using trigonometric functions. Specifically, we use the sine function because it relates the opposite side of a right-angled triangle (which in this case is the vertical component) to the hypotenuse (the inclined force).
The formula to find the vertical component (V) is:
V = F sin(θ)
Where F is the magnitude of the force, and θ is the angle of the force above the horizontal.
We're given that the horizontal component (H) is 40 N, which means:
H = F cos(θ)
To find F, we can rearrange the expression to:
F = H / cos(θ)
Plug in the known values:
F = 40 N / cos(60°) = 80 N
Now we would use the sine function to find the vertical component:
V = 80 N sin(60°)
Calculating this gives:
V = 80 N * (\sqrt{3}/2)
V ≈ 69.28 N
Therefore, the statement that the vertical component is 17.32 N is False.