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Lebombo
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"Projection Using Dot Product" "Finding a Force" (Boat Problem)
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A 600 pound boat sits on a ramp inclined at 30 degrees. What force is required to keep the boat from rolling down the ramp?
Solution: Because the force due to gravity is vertical and downward, ou can represent the gravitational force by the vector F = -600j. To find the force required to keep the boat from rolling down the ramp, project F onto a unit vector v in the direction of the ramp, as follows.
v = cos30i + sin30j = [itex]\frac{\sqrt{3}}{2}i + \frac{1}{2}j[/itex]
[itex]w_{1}[/itex]= [itex]proj_{v}F[/itex] = -300([itex]\frac{\sqrt{3}}{2}i + \frac{1}{2}j[/itex])
Magnitude of force is 300.
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The question I have is why is vector v a unit vector? What determines that v should have a magnitude of 1?
Homework Statement
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A 600 pound boat sits on a ramp inclined at 30 degrees. What force is required to keep the boat from rolling down the ramp?
Solution: Because the force due to gravity is vertical and downward, ou can represent the gravitational force by the vector F = -600j. To find the force required to keep the boat from rolling down the ramp, project F onto a unit vector v in the direction of the ramp, as follows.
v = cos30i + sin30j = [itex]\frac{\sqrt{3}}{2}i + \frac{1}{2}j[/itex]
[itex]w_{1}[/itex]= [itex]proj_{v}F[/itex] = -300([itex]\frac{\sqrt{3}}{2}i + \frac{1}{2}j[/itex])
Magnitude of force is 300.
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The question I have is why is vector v a unit vector? What determines that v should have a magnitude of 1?