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Lebombo

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**"Projection Using Dot Product" "Finding a Force" (Boat Problem)**

## 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?