Explanation
We must write a sine equation for the height h of the point w from the ground.
Using the data of the problem, we make the following diagram:
From the diagram, we wee see that the height h of point W from the ground is:
[tex]h=h_0+y=6ft+y.[/tex]
Where:
• h_0 = 6ft is the height from the ground to the center of the windmill,
,
• y is the height of point W to the center of the windmill.
We see that height y is the opposite cathetus to angle θ, using trigonometry, we see that:
[tex]y=r\times\sin\theta=1.5ft\times\sin\theta.[/tex]
Where r is the radius of the blade.
Replacing the equation of y in the equation of h, we get:
[tex]h(\theta)=6ft+1.5ft\times\sin\theta.[/tex]
We have found the equation for the height of point W as a function of the angle θ.
When point W is in the position of the diagram, the angle θ is equal to zero, so we have:
[tex]h(0)=6ft+1.5ft\times\sin0=6ft+1.5ft\times0=6ft.[/tex]Answer
• The equation for the height of point W as a function of the angle θ is:
[tex]h(\theta)=6ft+1.5ft\times\sin\theta[/tex]
• When W is in the position of the diagram, we have θ = 0, so its height is:
[tex]h(0)=6ft+1.5ft\times\sin0=6ft[/tex]
