6.1bc.notebook
March 09, 2012
1. Find the unit vector in the direction of u = 7,­2 1. Find the component form of the vector with direction angle 145 degrees and a magnitude of 8.
1. Find the components of the vector v
with direction angle 120o and magnitude of 5.
VECTORS IN A PLANE day 2and 3
Direction Angle:
the angle θ that v makes with the positive x­axis
The components of v: v =
|v|sinθ
2. Find the direction angle of the vector u =
and v =
v
θ
|v|cosθ
The unit vector: 1
6.1bc.notebook
March 09, 2012
Application of Vectors
Practice:
Find the horizontal and vertical components of the
vector 2i ­ 3j.
Find the magnitude and direction angle of the
vector 2i ­ 3j
Velocity of a moving object is a vector.
Velocity has both magnitude and direction
1. An airplane is flying on a bearing of 110o
at 500 mph. Find the component form of the velocity.
(recall: bearing is the angle that the line of
travel makes with due north, measured clockwise)
2. A golf ball is hit at a 18o angle with the horizontal direction with an initial speed of 20m/sec.
3. A force of 40 lbs acts on a an object at an
angle of 40o. A second force of 60 lbs acts on the object at an angle of ­20o. Find the direction and
magnitude of the resultant force.
Find the component form of the initial velocity.
Explain the meaning of the horizontal and vertical components
2
6.1bc.notebook
4. A plane is heading due east at 450 mph. There is an 80 mph wind with a bearing of 50o. Find the actual bearing of the plane and its speed.
Journal: What is a direction angle of a vector?
How do we use it to find the horizontal and
vertical components?
March 09, 2012
Practice:
5. A ship is heading due south at 10 mph. The current is flowing northeast at 3mph. Find
the actual bearing and speed of the ship. Journal: What does it mean to find the bearing of
a plane? 3