Choose your zero and your plus
Origin and positive direction are chosen for convenience.
Where do we start counting?
A ball was dropped from a height. In one drawing the origin is on the ground, in another it is at the point where the ball was let go.
The ball is at the same place in both drawings. Do you think it has the same number for its position?
What this lesson covers
The idea
The origin and the positive direction can be chosen as per convenience, but once chosen they must not be changed while solving a problem.
Where do we start counting?
A ball was dropped from a height. In one drawing the origin is on the ground, in another it is at the point where the ball was let go.
The ball is at the same place in both drawings. Do you think it has the same number for its position?
- No, the number can change with the choice
- Yes, the same number
- No, because the ball moves between the two drawings
Change the choices
Use the buttons. Say this is a ball that was dropped from 45 m above the ground and is now 20 m above the ground.
The ball did not move
With the origin on the ground and up positive, the ball was at +20 m. With down positive it was at −20 m. With the origin at the release point and down positive it was at +25 m, since it was 25 m below the release point. The ball stayed in the same place, only the numbers changed. That is allowed, but a choice must not be changed in the middle of a problem.
The origin and the positive direction can be chosen as per convenience. However, once chosen, they must not be changed while solving a problem.
Notes
Choose the origin and the positive direction as convenient, but do not change them once chosen, while solving a problem.
Check yourself
A ball is 20 m above the ground. With the origin on the ground and up as positive, its position is…
Same ball, origin on the ground, but down is taken as positive. Its position is…
The origin is the release point and down is positive. The ball is 25 m below the release point. Its position is…
What is the rule about choosing the origin and the positive direction?
- −20 m. A minus sign would mean 20 m in the negative direction, which is down here.
- +45 m. 45 m is the height of the release point. The ball is 20 m above the ground.
- +20 m — correct. Yes!
- −20 m — correct. Yes!
- +20 m. Up is now negative, so a place above the origin has a minus sign.
- 0 m. 0 m would be the position of the origin itself, which is on the ground.
- −25 m. Down is positive here, and the ball is below the origin, so the sign is plus.
- +25 m — correct. Yes!
- +20 m. 20 m is the height above the ground. Measured from the release point the ball is 25 m away.
- The origin must be on the ground. The book uses the ground as the origin in one figure and the release point in another.
- Change the positive direction whenever you like during a problem. Changing it midway would mix up the signs, so the choice must be kept until the problem is solved.
- Choose them as convenient, and do not change them while solving the problem — correct. Yes!