Magic orienteering by flickr user AlbeJTD

Vector Applications

General Notation for a Vector(1) Written using a lower case letter with an arrow on top.

Examples:

The magnitude of a vector is written as the absolute value of the vector.

Example:

(2) Written using two uppercase letters, from tail to tip, with an arrow on top.

Example:

Equivalent Vectors: Two vectors are equivalent if they have the same magnitude and direction; their relative position doesn't matter.

Example:

A

B

C

D

or=

=

Opposite Vectors: Two vectors are opposite if they have the same magnitude and opposite directions; their relative position doesn't matter.

Example:are opposite

and

The Zero Vector: Any vector with a zero magnitude is called a zero vector. The sum of two opposite vectors is also a zero vector. The zero vector is parallel to every other vector.

A large black ant pulls a breadcrumb N32°E with a force of 0.03 N. A small red ant pulls with a 0.045 N force in the direction E5°S. Determine the magnitude and direction of the resultant force.

A large black ant pulls a breadcrumb N32°E with a force of 0.03 N. A small red ant pulls with a 0.045 N force in the direction E5°S. Determine the magnitude and direction of the resultant force.

A large black ant pulls a breadcrumb N32°E with a force of 0.03 N. A small red ant pulls with a 0.045 N force in the direction E5°S. Determine the magnitude and direction of the resultant force.

The Tools of the Trade: Some Trigonometric Equations ...

The Pythagorean Theorem

A

B C

bc

a

The Sine LawA

B C

bc

a

The Cosine LawA

B C

bc

a

Some Useful Properties of Angles ...

Opposite Angles

a°a° b°b°

When two lines intersect, the angles opposite each other at the point of intersection are congruent.

Mnemonic: X

Alternate Angles

a°

a°b°

b°

Angles on alternate sides of a transversal are congruent.

Mnemonic: Z

Corresponding Angles

a°

a°b°

b°

Angles on coresponding sides of a transversal are congruent.

Mnemonic: F

A large black ant pulls a breadcrumb N32°E with a force of 0.03 N. A small red ant pulls with a 0.045 N force in the direction E5°S. Determine the magnitude and direction of the resultant force.

A large black ant pulls a breadcrumb N32°E with a force of 0.03 N. A small red ant pulls with a 0.045 N force in the direction E5°S. Determine the magnitude and direction of the resultant force.

A large black ant pulls a breadcrumb N32°E with a force of 0.03 N. A small red ant pulls with a 0.045 N force in the direction E5°S. Determine the magnitude and direction of the resultant force.

A man walks 350 m north, then 175 m east, and then 150 m south. How far and in what direction is he from his starting point? Round your answers to the nearest whole numbers.

Jack jogs north at 15 km/h for 30 minutes, and then turns east and jogs at 12 km/h for 20 minutes.

(c) In what direction does he need to go to return directly to his starting point?

(b) How far is he from his starting point?

(a) How far has he jogged in total?

An airplane is flying with a heading of 150° and an airspeed of 550 mph. The airplane is flying through a jet stream which is moving 175 mph with a heading of 80°. What is the velocity of the airplane with respect to the ground?

An aircraft is flying at a rate of 600 km/h with a bearing of 60°. A 100 km/h wind is blowing in the direction of 270°. Calculate the groundspeed and direction of the aircraft. Round your answer to the nearest whole numbers.