What are the x and y components of each vector? and the sum V1 + V2?

Question

1. Vector V1 is 8.66 units long and points along the negative x axis. Vector V2 is 5.31 units long and points at +55.0° to the +x axis.

(a) What are the x and y components of each vector?
V1x =
V1y =
V2x =
V2y =

(b) Determine the sum V1 + V2.

Magnitude=.......

Direction=........° (counterclockwise from the +x axis is positive)

Please help me to do this problem..i really don't get it Thanks :))))))

Answer 1

V1x= -8.66 units
V1y=0 units
V2x=+3.05 units( 5.31 * cos 55 deg.)
V2y=+4.354 units(5.31* sin 55 deg.)
(b) vector sum v1+v2 can be calculated as follows:-
along x axis:
Vxtotal=3.05-8.66= -5.61 units
Vy total=+4.354 units

Vnet=sqrt of(Vx^2 + vy^2) =7.10 units

Magnitude=7.10 units

direction=180 deg. minus tan inverse of 0.776 from pos. x axis


was the answer correct?

!

Answer 2

Assuming that V1 starts at the origin and becomes more negative X1 is -8.66 units and Y1 is 0 units. Assuming that the X-axis is 0° and the Y-axis is 90°, theta is 55°. That makes X2=8.66*COS 55°=4.97 units long and Y2=8.66*SIN 55°=7.09 units long. The sum V1+V2=(X1+X2 and Y1+Y2). X1+X2=-8.66+4.97=-3.69. Y1+Y2=0+4.97=7.09. V2 is the square root of V2x and V2y.
V2 = (-3.69^2+7.09^2)^0.5
= (13.61+50.27)^0.5
= 7.99
The direction is given by the arc tangent (theta) of Y/X. Theta=arctan(Y/X)
arctan(7.09/-3.69)
arctan(-1.92)=-62.5°.
This places the answer in the fourth quadrant (positive X and negative Y). I would put the answer in positive form by adding 360 degrees to it. -62.5°+360°=297.5°, which is in the fourth quadrant (270° to 260°).
Answers: a) V1x = -8.66 V1y = 0 V2x = 4.97 V2y= 7.09
b) V2x = -3.69 V2y = 7.09 V2 = 7.99 Vtheta = 297.5°.