A vector in the xy plane has a magnitude of 25 and an x component of 12.

Question

Topic: Physics Posted 9 months ago

A vector in the xy plane has a magnitude of 25 and an x component of 12. The angle it makes with the
positive x axis is:

A) 26
B) 29
C) 61
D) 64
E) 241

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Mar 10, 2024

Koala Ai Support

The angle θ that a vector makes with the positive x-axis can be found using the x and y components of the vector.

Given that the x component is 12 and the magnitude of the vector is 25, we can use the formula:

tan(θ) = y / x

Where y is the y component of the vector. We can find y using Pythagoras' theorem:

y = √(25^2 - 12^2)
y = √(625 - 144)
y = √481
y ≈ 21.9

Now, we can find the angle θ using:

tan(θ) = 21.9 / 12
θ = arctan(21.9 / 12)
θ ≈ 61 degrees

Therefore, the angle the vector makes with the positive x-axis is 61 degrees.

So, the correct answer is:

C) 61

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