Question

dissplacement vector A is 4.5 km North, vector B is 3.0 km 50 degrees N of W. Find their resultant

Answer 1

vector A is 4.5 Km N, this means that for this vector we are not going to have an x- coordinate, we are only going to have a y- coordinate , since this vector is going N then the y- cordinate is postive number, and the y-coordinate for this vector will be + 4.5, while the x-vector is going to be 0
vector B is 3 Km 50 degrees N of W, this simply means 3 Km W50N , for vector B, since the object is moving both in the x- direction and the y- direction then we are going to have an x- cordinate and a y- coordinate for this vector, also since the directions that this vector has are N and W , threrefore this means that we are going to have a negative x- coordinate ( because the object is going to the west in terms of the horizontal direction) and a postive y- coordinate( since the object is going north in terms of the vertical direction)
in order to find coordinates for the second vector in terms of x and y: (- 3x cos50 , +3 sin50)
= (-1.928, 2.298)
then we are going to add both vectore together
( 0,4.5) +
(-1.928, 2.298)
=( -1.928, 6.798)
we are going to use the pythageorm theorm to find the resultant displacment, we are going to call it h
h^2=x^2+y^2
h^2= (-1.928)^2 + (6.798)^2
h^2= 49.931
h= 7.06 Km
then we know that the oject travelled a resultant displacment 7.06 Km, but we need to know in which direction did the resultant vector traveled.
from the sum of the 2 vectors: (-1.928,6.798) we know that we have a negative x- cordinate which means we are going west horizontaly , for the y-coordinate we have a postive value which means we are going north verticaly) we are going to use H to find the angle in which the resultant vector is sin^-1( 6.728/7.60)= 62.72
therfore the final resultant is 7.60 Km w62.2 N

Answer 2

Hey umm, isnt h=7.06 instead of 7.6(?)

Answer 3

7.07