vectors and magnitude?

Question

please explain

Given two vectors, one has a magnitude of 3 meters and a direction of 10 degrees and the second has magnitude of 5 meters and a direction 30 degrees. What is the magnitude and direction of their sum? The angles in this problem are relative to the positive x axis.

Answer 1

find the x and y component of vector 1.
vx1=cos(10)3=2.95m
vy1=sin(10)3=.52m

Find the x and y components of vector 2
vx2=cos(30)5=4.33m
vy2=sin(30)5= 2.5m

add up all x's and y's component.
x's=2.95+4.33=7.28
y's= 2.5+.52=3.02

draw a new triangle
a^2+b^2=c^2
7.28^2=3.02^2=c^2
c=7.88m

theta= tan^-1(3.02/7.28)
theta=22.53 degrees

Answer 2

best way it to draw the question on a graph paper on scale and find the magnitude of the resultant.

the above vectors cannot be added together, as theyboth originate from teh origin (say)

you need to solve the triangle first, one angle of the triangle is 30-10=20degress and hte sides of the tirangle are 3 and 5

[ a right angles tirangle has sides in the ratio 3:4:5, so here i guess since two components are present, 3 and 5 so the other side can be 4 and thus one angle has to be 90deg, thus the third angle is 180-90-20=70degrees ]

Answer 3

to do this problem, you must break down each vector into two components (x & y), then add them together, respectively. then solve for the resulting x & y components.
for the first one...
sin(10) = opp/3
implies opp. length(y-comp) = 3sin(10)...
now for the x-comp, cos(10) = adj/3
implies adj length(x-comp) = 3cos(10)...
repeating the same proceduer for the 30degree vector...
y-comp = 5sin(30) = 5(1/2) = 5/2
x-comp = 5cos(30) = 5(sq.rt(3)/2) = 5(sq.rt(3))/2
now adding the components together respectively you get...
new y-comp = 3sin(10) + 5/2 equivelent to 3.021
new x-comp = 3cos(10) + 5(sq.rt(3))/2 equiv. to 7.285
to get the new angle, use the inverse tangent...
tan(angle) = opp/adj = y-comp/x-comp = 3.021/7.285
now the angle = tan(-1)(3.021/7.285) = 22.523 degrees
to get the magnitude, simply use the pathag. theorem...
mag = sq.rt((3.021)^2 + (7.285)^2) = 7.887

the final answer is 7.887 meters at 22.523 degrees with respect to the x-axis

Answer 4

Split the two vectors up into x and y components:

Vector 1 (3m at 10 degrees)
x1 = 3cos(10)
y1 = 3sin(10)

Vector 2 (5m at 30 degrees)
x2 = 5cos(30)
y2 = 5sin(30)

Sum Vector (add up the components):
x = 3cos(10) + 5cos(30)
y = 3sin(10) + 5sin(30)

Magnitude = sqrt(x^2 + y^2)
Angle = atan(y/x)

Answer 5

first u have to find the x and y components. first vector (V1)
vx= 3 ( cos 10) vy=3(sin10)

then the other one V2

v2x= 5 cos30 v2y= 5 sin30= 5/2=2.5

then add all the vx and all the vy.
V= squareroot of (vx)^2 + (vy)^2