Calculating Components

Vector Projections It often becomes necessary to find the projection of one vector across the length of another. When this is required, the procedure is denoted as: Calculating Components of U along V The component of u along v is defined as:

Calculate the following components of u along v 1. and 2. and

Work Problems Work Done The work W done by a force F in moving along a vector D is:

Let’s try it! A force is given by the vector F = and moves an object from the point (1,3) to the point (5,9). Find the work done. - First we calculate the Displacement vector D -Now we calculate So the work done is 26 ft-lbs.

Pulling a Wagon A man pulls a wagon horizontally by exerting a force of 20lbs. On the handle. If the handle makes an angle of 60 degrees with the horizontal, find the work done in moving the wagon 100ft. -Displacement vector. The force on the handle can be written as:

This gives us two vectors to work with: Now we can find the Work done: