An 8-m boom is used to move a bundle of piping from point A to point B. Determine the exact vertical displacement of the of the boom when the operator moves it form 30 degrees to 60 degrees.
(Just need work checked)
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I drew two triangles to solve this.
The first triangle:
sin30 = opposite/hypotenuse
x = 8/2
x = 4 <----- First vertical distance
The second triangle
sin60 = opposite/hypotenuse
y = 8 * root3/2
y = 4 root3 <-----second vertical distance
Vertical displacement = y -x
Vertical displacement = 4 root3 - 4 <-----
looks good to me
Thank you
To determine the exact vertical displacement of the boom, you correctly used the sine function to calculate the opposite side (vertical distance) in two different triangles.
In the first triangle, you applied the sine function with an angle of 30 degrees and found that the vertical distance was 4 units.
In the second triangle, you applied the sine function with an angle of 60 degrees and found that the vertical distance was 4√3 units.
To calculate the vertical displacement, subtract the initial vertical distance (4 units) from the final vertical distance (4√3 units).
Vertical displacement = (4√3 units) - (4 units)
You did the calculation correctly, and the answer is indeed 4√3 - 4 units.
Therefore, the exact vertical displacement of the boom when the operator moves it from 30 degrees to 60 degrees is 4√3 - 4 units.