Pre-Calculus Honors
Unit 9 Lesson 4
Name:
Period # _____
Unit 9 Lesson 4: Do Now v = 4i – j
a.) Find the directional angle of the vector.
b.) Find a vector in the same direction as v that has a magnitude of 6.
Name:
Period # _____
Unit 9 Lesson 4: Do Now v = 4i – j
a.) Find the directional angle of the vector.
b.) Find a vector in the same direction as v that has a magnitude of 6.

Pre-Calculus Honors
Unit 9 Lesson 4
Pre-Calculus Honors
Unit 9 Lesson 4
Application of Vectors
Objective: ______________________________________________________________
1.
Guided Practice: Using Vectors to find speed and direction
Verbal
An airplane is traveling at a speed of 500 MPH with a bearing of 330 degrees at a fixed altitude with negligible wind velocity.
The bearing is the angle measured, starting from the
North , going clockwise .
As the airplane reaches a certain point, it encounters a wind blowing at 75 MPH in the direction 45 degree NE.
Find the resulting speed and direction of the airplane.
Diagram
Directions: Draw a velocity vector that represents the plane’s velocity with negligible wind, a velocity vector that represents the wind’s velocity, and resulting velocity vector when the plane encounters the wind.
Plane’s Velocity Vector Wind’s Velocity Vector
Algebraic
Directions: Write the vector in component form by finding the horizontal and vertical components.
1.
Find the component form of the plane’s velocity with no wind.
2.
Find the component form of the wind’s velocity.
3.
Find the component form of the plane’s velocity affected by the wind.
Plane’s and Wind’s
Velocity Vector
Communication
1.
Find the resulting speed of the plane.
2.
Find the resulting direction of the plane.
Draw a diagram if necessary.
3. Analyze the speed and direction of the plane in the context of the situation.

Pre-Calculus Honors
Unit 9 Lesson 4
Vector Real World Applications Problem Set
1.) An airplane is flying on a compass heading (bearing) 340

at 325 mph. A wind is blowing with bearing 320

at 40 mph. Find the resulting speed and direction of the plane.
2.) A quarterback is running forward at 5 meters per second and throws the football with a velocity of 25 meters per second at an angle of 40 degrees from the horizontal. What is the resulting speed and direction of the pass?
3.) A force of 60 1b. acts on an object at an angle of 40 degrees. A second force of 85 lb. acts on an object at an angle of -35 degrees. Find the magnitude and direction of the resulting force.
Homework: Finish Problem Set #1 – 3.

Pre-Calculus Honors
Unit 9 Lesson 4
Challenge: To pull luggage, Greg exerts a force of 150 newtons at an angle of
58 degrees with the horizontal. If the resulting force of the luggage is 72 newtons at an angle of 56.7 degrees from the horizontal, what is the magnitude of the resultant Force of friction and Force of weight. Refer to the diagram below.