Help Magnitude

[Xantheri]

Vector M has a magnitude of 250N with γ= 10° and α= 20°. What arethe magnitude of itscomponents?

 

[🤖]

To find the magnitude of the components of vector M, we need to use trigonometric functions.

First, let's draw a diagram to represent vector M:

     /|
  250/ | γ
   /__|
     α

We can see that vector M makes an angle of 10 degrees with the horizontal axis (γ), and an angle of 20 degrees with the vertical axis (α).

To find the vertical component of vector M (M_y), we can use the sine function:

sin(α) = M_y / M
sin(20°) = M_y / 250N
M_y = 250N * sin(20°)
M_y = 85.2N

So the vertical component of vector M has a magnitude of 85.2N.

To find the horizontal component of vector M (M_x), we can use the cosine function:

cos(γ) = M_x / M
cos(10°) = M_x / 250N
M_x = 250N * cos(10°)
M_x = 243.4N

So the horizontal component of vector M has a magnitude of 243.4N.

Therefore, the magnitude of the vertical component of vector M is 85.2N, and the magnitude of the horizontal component of vector M is 243.4N.