What is the magnitude of a vector that makes an angle of 85º to the x -axis and whose x component is 12 m?
is it 137.7? The number I got seems to be a bit too big...
v cos 85 = 12
v = 12 / cos 85 = 12/ 0.087 = 13.9 we agree
if it is at almost 90 degrees to the x axis the of course the y component will be much greater than the x component.
Well, I'm not sure about the exact magnitude of the vector, but I can tell you this: it definitely won't fit in your pocket! With that angle and the x component, the vector is strutting around like a peacock. It's probably partying with some pretty big values. But hey, don't worry, it's all about the size, right?
To determine the magnitude of a vector, you can use the following formula:
Magnitude (|v|) = √(v_x^2 + v_y^2)
In this case, the vector makes an angle of 85º to the x-axis, and its x-component is given as 12 m.
To find the y-component of the vector, we can use trigonometry. The relationship between the x and y components of a vector and its angle to the x-axis can be expressed as follows:
v_x = |v| * cos(θ)
v_y = |v| * sin(θ)
Given that the angle (θ) is 85º and the x-component (v_x) is 12 m, we need to solve for the y-component (v_y).
v_y = |v| * sin(85º)
Now, we can substitute these values into the magnitude formula:
|v| = √((12^2) + (v_y^2))
To calculate the y-component (v_y), we use:
v_y = |v| * sin(85º)
Now, we can find the magnitude (|v|):
|v| = √((12^2) + (|v| * sin(85º))^2)
To solve this equation, we can simplify it by squaring both sides:
|v|^2 = (12^2) + (|v| * sin(85º))^2
|v|^2 = 144 + (|v|^2 * sin^2(85º))
Subtracting (|v|^2) from both sides:
0 = 144 + (|v|^2 * sin^2(85º)) - |v|^2
Now, we can isolate (|v|^2) by moving the other terms to the opposite side:
|v|^2 * sin^2(85º) - |v|^2 = -144
Factoring out (|v|^2):
|v|^2 * (sin^2(85º) - 1) = -144
Dividing both sides by (sin^2(85º) - 1):
|v|^2 = -144 / (sin^2(85º) - 1)
Now, we can calculate the magnitude (|v|) using this equation.