1. how do you add two vectors using heard -to -tail method?

Question

question 2.
vector a has a magnitude 10 and makes an angle of 75 degrees with x-axis. Calculate X and Y components of vector a.

Answer 1

Question 1
Vector V1 = ( a , b )
Vector V2 = ( c , d )
V1 + V2 = [ ( a + c ) , ( b + d) ]

---->a
------>c
---------->a + c

similarly for b + d (vertical components)

Question 2
Components are:-
Horizontal
X = 10 cos 75° = 2.59
Vertical
Y = 10 sin 75° = 9.66

Answer 2

just visualize a triange. In this case your vector is the hypotenuse equal to 10 units in length. Imagine

...................C
....................|
....................|
....................|
A--------------B

(ignore all the dots above - it was the only way I could draw my triangle!!)
The line AC is 10 units. The angle CAB is 75 degrees. So using trig identities:

opposite/hypotenuse = sin theta
BC / AC = sin 75
BC / 10 = sin 75
BC = 10* sin 75
BC = 9.66

adjacent/hypotenuse = cos theta
AB / AC = cos 75
AB / 10 = cos 75
AB = 10* cos 75
AB = 2.59


Or you can use Pythagorean theorem:

AB^2 + BC^2 = AC^2
AB^2 + 9.66^2 = 10^2
AB^2 = 10^2 - 9.66^2
AB^2 = 6.68
AB = 2.59

So, the x-component is AB and is 2.59; the y-component is BC and is 9.66

Answer 3

x = 10cos75= 2.5882
y = 10 sin(75) = 9.6593

Answer 4

Check this link for the solution

http://img523.imageshack.us/img523/3480/vectorsca9.png