Unit 2 - Objective 4 - Application of Vectors
Quick Review

Example 1

A truck weighing 22,500 lbs is on a 25° hill. Find the components of the truck's weight parallel and perpendicular to the road.

Solution:

The weight of an object (truck) is the gravitational force with which earth attracts it. This forces always acts vertically downward and is indicated by the vector w. The components of w are F1 and F2. Because w is vertical and F2 is perpendicular to the road, the angle between w and F2 is equal to the angle the road makes with the horizon. Using trigonometric functions:

F1 = w sin = 22,500 sin 25° = 9,509 lbs

F2 = w cos = 22,500 cos 25° = 20,392 lbs

So the components of the truck are 9,509 lbs parallel to the road and 20,392 lbs perpendicular to the road.

Example 2

If the truck rolls down the hill at 15mph, find the magnitudes of the horizontal and vertical components of the truck's velocity.

Solution:

The horizontal and vertical components of vector V are Vh and Vv.

Vh = V sin 25° = 15 sin 25° = 6.3 mph

Vv = V cos 25° = 15 cos 25° = 13.6 mph

Example 3

Two forces, F1 and F2, act on an object. If F1 is 40 lbs, F2 is 75 lbs, and the angle between them is 50°, find the magnitude and direction of the resultant force.

Solution:

Sketch the two forces as vectors and place the object at the origin.
vectorhorizontal
component

vertical
component
F140.0
0.0
F275 cos 50° = 48.2
75 sin 50° = 57.5
RRx     88.2
Ry     57.5

So, Rx = 88.2 and Ry = 57.5

The magnitude of R is: