x^2+y^2=v^2
sqrt((40.428649 m/s)^2 +(19.428649 m/s)^2) = 44.854744 m/s = v
You draw the arrowhead on the arrow head going up and to right in this case.
2. Break into components using the sine and cosine rules...
sin 68° = xcomp1/100 km/h
xcomp1 = 92.7183855 km/h
cos 68° = ycomp1/100 km/h
ycomp1 = 37.4606593 km/h
sin 65° = xcomp2/145 km/h
xcomp2 = 131.414629 km/h
cos 65° = ycomp2/145 km/h
ycomp2 = 61.279648 km/h
Find the components of the third vector by summing up respective components. NOTE: The x components are going in opposite directions, so you need to subtract one from the other, in this case, the direction you do this in isn't important as you'll just get the negative of the value you want and you'll be squaring it anyway in the pythagorean theorem, yielding the same value. Just watch your signs if you're doing this with three or more vectors in the future (vectors going in the same direction in a certain component direction must have the same sign when you sum all the components).
y = 37.4606593 km/h + 61.279648 km/h = 98.7403073 km/h
x = 92.7183855 km/h - 131.414629 km/h = -38.6962435 km/h
Now using the pythagorean theorem...
x^2+y^2=v^2
v = sqrt((98.7403073 km/h)^2 + (-38.6962435 km/h)^2) = 106.052098 km/h
You draw the arrow from the tail of the first vector to the arrowtip of the second (as a rule).
3. Technically, we can take arbitrary components to sum vectors in two dimensions, thus, tThis one is easier to do if we don't use x and y components but rather components in the direction of the first vector and components in the direction of orthogonal, or perpendicular to that direction, we'll call the former the z direction and the latter the w direction for this example.
By observation...
zcomp1 = 8 N
wcomp1 = 0 N
We can draw a right triangle to find the components of the second vector, using zw components, by drawing a vector in the w direction from the tip of the arrowhead in the second vector to the first vector...then using sines and cosines.
sin 41° = wcomp2/3 N
wcomp2 = 1.96817709 N
cos 41° = zcomp2/3 N
zcomp2 = 2.26412874 N
Following this we can sum up the components, NOTE that the z components are going in opposite directions...
z = 8 N - 2.26412874 N = 5.73587126 N
w = 0 + 1.96817709 N = 1.96817709 N
Now using the pythagorean theorem...
z^2 + w^2 = v^2
v = sqrt((5.73587126 N)^2 + (1.96817709 N)^2) = 6.06415206 N
Draw the arrow from the tail of the first vector to the arrowtip of the second.