Vector A has a magnitude of 3.0 m and direction 1o3 degrees relative to the positive x-axis. Vector B has magnitude 5.0m and direction 215 relative to the positive x-axis.

Question

Vector A has a magnitude of 3.0 m and direction 1o3 degrees relative to the positive x-axis. Vector B has magnitude 5.0m and direction 215 relative to the positive x-axis.

For the resultant
I did Rx= 3 cos 103 + 5 cos 215

Ry=3 sin 103 + 5 sin 215

Then sqrt Rx^2 + Ry^2 and got 4.77

1) The resultant R has direction?

less than 90 degrees
between 90 and 180
between 180 and 270
between 280 and 360

I do not know how to figure this out. Thank you.

Answer 1

Wasn't Rx something like -4.7

and Ry something like zero, but small positive? (I don't remember).

anyway, if Rx is negative, and Ry is slight postive, then theta is almost 180 deg.

Recheck Rx and Ry

Answer 2

so would it be between 90 and 180 or 180 and 270?

Answer 3

To determine the direction of the resultant vector R, you can use trigonometry. Recall that the direction of a vector is typically measured counterclockwise from the positive x-axis.

First, calculate the x-component of the resultant vector (Rx) using the formula: Rx = Ax + Bx, where Ax and Bx are the x-components of vectors A and B, respectively.

Rx = 3 cos(103°) + 5 cos(215°)
(Note: Make sure to convert the angles to radians if your calculator is set to radian mode)

Next, calculate the y-component of the resultant vector (Ry) using the formula: Ry = Ay + By, where Ay and By are the y-components of vectors A and B, respectively.

Ry = 3 sin(103°) + 5 sin(215°)

Now that you have the components of the resultant vector, you can find its magnitude (R) using the formula: R = sqrt(Rx^2 + Ry^2).

R = sqrt(Rx^2 + Ry^2)

After calculating the magnitude of the resultant (which you have already done and got 4.77), you can find its direction by calculating the angle theta (θ) using the formula: θ = tan^(-1)(Ry / Rx).

θ = tan^(-1)(Ry / Rx)

In this case, if you substitute the calculated values of Rx and Ry into the formula, you will get the angle θ. Then, you can compare the calculated angle θ to the given options of the question (less than 90 degrees, between 90 and 180, between 180 and 270, between 280 and 360) to determine which range it falls into.

Hope this helps!