The two vectors and in the figure below have equal magnitudes of 7.0 m and their angles are θ1 = 30° and θ2

Question

The two vectors and in the figure below have equal magnitudes of 7.0 m and their angles are θ1 = 30° and θ2 = 95°.

a) Find the x and y components of their vector sum r.

(b) Find the magnitude of vector r.

(c) Find the angle vector r makes with the positive x axis

Answer 1

This question can't be answered for you by someone else without seeing the diagram, or at least giving a better description of it. The sum vector depends on whether they go in similar directions or opposite directions.

However, if you follow these steps, you may be able to find the answer on your own. First of all, if you are going to find the sum vector, you can copy the second vector onto the end of the first vector, so that you can follow the first one to the end, then follow the second one, and see what the result is. If you can successfully graph this, you can find the coordinates of the endpoints of r, and also its magnitude and angle.

Good luck!

Answer 2

rx = 3.5sqrt(3) -sin(5) = 6.062-.087= 5.98
ry = 3.5 + 7cos(5) = 3.5 + 6.97 = 10.47

mag = sqrt(5.98^2+10.47^2) = 12.06m

angle = arctan 10.47/5.98 = 60.27 degrees