2. Vector Addition (1-dimensional vectors)
Adding 1-dimensional Vectors
I am swimming downstream in a river.
The speed of the river current is 0.25 m/s, as indicated by the length and direction of the blue arrow in the vector diagram.
I swim downstream at the rate of 1 m/s, as indicated by the dark red arrow below. (It is `4` times the length of the river current vector, indicating that my swimming velocity is `4` times the velocity of the river current.)
Our friends are on the riverbank watching me swim. They observe that I am moving quite quickly. My velocity is:
1 + 0.25 = 1.25 m/s.
The river is helping me to move quickly relative to the people watching. This is an example of vector addition.
We can show this on our diagram as follows:
The equivalent vector (1.25 m/s downstream) is shown in pink:
The diagram illustrates the boost that I am getting from the river current and demonstrates my total speed, relative to the riverbank, of:
1 + 0.25 = 1.25 m/s.
The Return Journey (Subtraction of Vectors)
To get back to my friends, I need to swim against the current so my speed relative to the people who are watching me will be less. My velocity relative to the river bank is now:
1 − 0.25 = 0.75 m/s.
The 2 vectors are now acting in opposite directions.
An equivalent way of drawing our 2 vectors is to put the tail of the current vector next to the tip of the swimming vector as follows:
My velocity relative to the people watching (0.75 m/s, upstream) is shown in pink:
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Math Lessons on DVD
Easy to understand math lessons on DVD. See samples before you commit.
More info: Math videos