How do you find the component form of the sum of u and v with direction angles deta_u and deta_v?

Question

I'm only given the following information and I'm not sure what to do...
magnitude; || u || = 5
|| v || = 5
angle; deta_u = 0 degree
deta_v = 90 degree

so which one is correct?
Critical Mass or Jimbu?

Answer 1

the total velocity is the vector sum of the two component velocities. since ||u|| only contributes in the x-direction and ||v|| only contributes in the y-direction, the total velocity is:

v = 5i + 5j

where "i" indicates the x-direction and "j" indicates the y-direction.

to find the masgnitude of the total velocity, simply take the square root of the sum of the squares, and the direction is the arctan of ||v||/||u||:

magnitude = sqrt(5^2 + 5^2) = sqrt(50)

direction = arctan(5/5) = 45 degrees.

Answer 2

A vector can also be written in component form as:

M

where M is the magnitude and θ is the angle (measured from the positive x-axis).

So:

u = 5 = 5 <1 i + 0 j> = <5 i + 0 j>

v = 5 = 5 <0 i + 1 j> = <0 i + 5 j>

Then

u + v = <5 i + 0 j> + <0 i + 5 j> = <5 i + 5 j>, in component form.

----

Eh...Not sure why Hy emphasizes the first answer... component form is the i's and j's, not the magnitude and angle....?

Answer 3

First answer is correct.

In general, if the angle isn't a simple multiple of a rightangle, you get the components this way:

Using i and j as the first answer did,
if the magnitude of the vector is v and the angle is A, then

i component = v cosA; j component = v sinA.

So between them your given vectors contribute 5 in the i direction (u) and 5 in the j direction (v). The rest is as the first answer said.

Answer 4

ok i think i just learned something....thx