Answer:
It should be mentioned that an efficient way to work this vector addition problem is with the cosine law for general triangles (and since
a
,
b
and
r
from an isosecles triangle, the angles are easy to figure). However, in the interest of reinforcing the usual systematic approach to vector addition, we note that the angle
b
makes with the +x axis is 30
0
+105
0
=135
0
(a) The x component of
r
x
=(10.0m)cos30
0
+(10.0m)cos135
0
=1.59m
(b) the y component of
r
is r
y
=(10.0m)sin135
0
= 12.1 m.
(c) the magnitude of
r
is r = ∣
r
∣=
(1.59m)
2
+(12.1m)
2
=12.2m
(d) The angle between
r
and the +x direction is tan
−1
[(12.1m)/(1.59m)]=82.5
0
Explanation:
