A boy walks 20 m [E 35oS] then 40 m [E 50oN]. Determine his net displacement.
I know this is a simple question but I am having trouble with which angle goes parallel with which side.
The answer to this is to find the x components and then the y components and then use the pythagorean theorem to solve it. In this case:
Displacement X= 20sin(35o)+40sin(50)
Displacement Y= 20cos(35o)+40cos(50)
Displacement vector= sqrt(Displacement X^2 + Displacement Y^2)
@zxcvbnm1216 Coldsummer1’s main approach is right. But I’m not very familiar with the notation you used for heading. Does E 35° S mean 35 degrees towards the south, relative from east (i.e. heading of 125°)? If so, I feel like the y-coordinate displacements should have opposite signs.
Yes, E 35° S mean 35 degrees towards the south, relative from east (i.e. heading of 125°). Would that mean that the y-coordinate displacement should have different sides. Is there a different way to do this question? @MITer94
@zxcvbnm1216 I recommend splitting both vectors into x- and y-components and combining them as @Coldsummer123 did (except the y components should differ in sign).
You could also solve by applying the law of cosines, but I recommend the first method.
how would you solve using the law of cosines?
Edit: Nvm thought law of cosines was law of sines for a sec
@Coldsummer123 granted, it can be solved using only the law of sines, but why anyone would want to do so is beyond me. 
Thank you @Coldsummer123 @MITer94 So what you are saying @MITer94 is that the displacement of y would be Displacement Y= 20cos(35o)-40cos(50) or do I have it backwards?
@zxcvbnm1216 It also depends on your choice of coordinate system.
Using a 90 degree heading (east) as the +x axis, and a 0 degree heading (north) as the +y axis, the y-component of displacement is actually -20 sin 35 + 40 sin 50 (you should look at the sides opposite these angles and what they represent).
ok thanks @MITer94 . I can see that it has to do with the 360 degrees grid and how the one side is negatvie
logically the answer I am getting is wrong @MITer94 unless I drew it out wrong. This is what I got
Displacement x-> -20sin35 + 40 sin 50 = 19.2
Displacement y -> 20cos 35 - 40 sin 50= 42.1
Displacement vector -> root (42.1 squared + 19.2 squared)
Displacement vector -> 46.3 m
Does this make sense?
@zxcvbnm1216 that’s not what I got. Where did you get 40 sin 50 from (in both Dx and Dy)?
shoot you are right @MITer94 it is supposed to be cos for displacement y