The vector below has a magnitude of 6.60 N and is pointing in a direction of 325 degrees counterclockwise from the positive x axis. What are the x and y components of the vector?
Question
The vector below has a magnitude of 6.60 N and is pointing in a direction of 325 degrees counterclockwise from the positive x axis. What are the x and y components of the vector?
Solution
To find the x and y components of the vector, we can use the equations:
X = rcos(θ) Y = rsin(θ)
where r is the magnitude of the vector and θ is the angle it makes with the positive x-axis.
Given that r = 6.60 N and θ = 325 degrees, we can substitute these values into the equations.
However, the trigonometric functions in most programming languages and calculators use radians, not degrees. So, we first need to convert the angle from degrees to radians.
1 radian = 180/π degrees So, θ = 325 * π/180 = 5.68977 radians
Now we can find the x and y components:
X = 6.60 * cos(5.68977) = -2.68 N Y = 6.60 * sin(5.68977) = -6.06 N
So, the x and y components of the vector are -2.68 N and -6.06 N, respectively.
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