A lawn sprinkler spins in a circle. The sprinkler covers a radius of 12 feet. Which choice is the closest to the area of lawn th
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Answer:
The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.
Step-by-step explanation:
We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have
And apply it to get the horizontal and vertical displacements.
Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.
Linear displacements.
Using the definition of displacement, we can write the horizontal displacement as
So we can use the given points on the displacement formula
In the same manner we can look at the y components of those points to find the vertical displacement
Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.
Projection angle.
The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write
Solving for the angle we get
Replacing values
Which give us
So the projection angle is 39.3 degrees.