A vector has a magnitude of 50m and is pointing to the right, 30 degrees below the horizontal. What is the vertical component of this vector?
Question
A vector has a magnitude of 50m and is pointing to the right, 30 degrees below the horizontal. What is the vertical component of this vector?
Solution
The vertical component of a vector can be found using the formula:
V = M * sin(θ)
where: V is the vertical component, M is the magnitude of the vector, and θ is the angle the vector makes with the horizontal.
Given in the problem, M = 50m and θ = 30 degrees.
However, since the vector is pointing below the horizontal, we take the angle as negative. So, θ = -30 degrees.
Now, plug these values into the formula:
V = 50m * sin(-30 degrees)
Using the sine of -30 degrees (-0.5), the calculation becomes:
V = 50m * -0.5
So, V = -25m
The negative sign indicates that the vector is pointing downwards. So, the vertical component of the vector is -25m.
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