Question

another vector addition: give that R(100,45°) and F1(a,0°) and F2(b,70°) find a and b.

Answer 1

okay these are the things we know:
R^2=(Rx)^2 +(Ry)^2
tan45°= Ry/Rx
F1x=a F2x=bcos70° F2y=bsin70°

Answer 2

right? @Carl_Pham @waterineyes @shubhamsrg

Answer 3

seems legit..

Answer 4

okay, so then what would be the best thing to find first?

Answer 5

i'll go offline.. if someone can solve it step by step.. i'll really appreciate it :)

Answer 6

100cos45 = a + bcos70
100sin45 = bsin 70

just solve these 2..

Answer 7

Find the components of R first.

R_x = 100 cos(45) = 50 r2.
R_y = 100 sin(45) = 50 r2.

Now lets see how those are related to the components of F1 an F2:

F1_x + F2_x = R_x
F1_y + F2_y = R_y

Substituting in what we know:

F1_x + F2_x = 50r2.
0 + F2_y = 50r2.

So now we know F2_y. For F1_x and F2_x we have one equation with two unknowns. Clearly we need another equation. Well, since we know F2_y, we can use the relationship between F2_y and F2_x:

tan(70) = F2_y/F2_x

So F2_x = F2_y/tan(70) = 50r2/tan(70).

Going back to our equation for the sum of F1_x and F2_x we can now solve for F1_x:

F1_x + 50r2/tan70 = 50r2

F1_x = 50r2 - 50r2/tan70.

Now we know F1_x, F1_y, F2_x, and F2_y, so we can construct the lengths of F1 and F2 from Pythagoras, e.g. sqrt((F1_x)^2 + (F1_y)^2) is the length of F1.

Answer 8

thank you!