# Sign Convention for Projectile Motion on an Inclined Plane

• Simon Hall
In summary, the conversation is about choosing a sign convention when dealing with projectiles on an inclined plane. The question is whether the x-direction should increase from left to right or from right to left, and if it affects the accuracy of the calculations. It is concluded that it does not matter which direction is chosen, as long as it is consistent throughout the calculations. The problem the person was having was due to not adjusting the landing angle formula when changing the sign convention.
Simon Hall
Hi, I have a quick question about projectiles on an inclined plane. Specifically, when the projectile is launched down an inclined plane. Is it not possible to use your choice of sign convention? If the projectile is moving from left to right like so:

V
...V
.....V
....__ V__

Could I not choose the x-direction as increasing from left to right just as easily as increasing from right to left?

In the first instance, increasing left to right, the initial velocity and acceleration due to gravity in the x-direction would both be positive, and in the second instance they would both be negative.

The trouble is: it only seems to work (I only get the "right" answer) when it's the former, Ux and Ax are +. Why is this the case, does anybody know?

It works whichever direction you choose for x. Write down your calculations and we can help you point out where it goes wrong.

Hello Simon,

Please post in the homework forum and use the template. Usually x is from left to right; no problem if you are consistent. But gravity often is only in the vertical direction, which we are used to call y !

Hi, thanks for the responses. I had thought so. I now realize that I was changing the sign convention without (correspondingly) altering the landing angle formula! Thanks.

## 1. How does the angle of incline affect the projectile's motion down an incline?

The angle of incline affects the projectile's motion by altering the force of gravity acting on the projectile. The steeper the incline, the greater the force of gravity acting on the projectile, resulting in a faster acceleration and a shorter distance traveled.

## 2. What is the relationship between the speed of the projectile and the angle of incline?

The speed of the projectile is directly proportional to the angle of incline. This means that as the angle of incline increases, the speed of the projectile also increases.

## 3. How does the mass of the projectile affect its motion down an incline?

The mass of the projectile does not directly affect its motion down an incline. However, a heavier projectile will experience a greater force of gravity, resulting in a faster acceleration and a shorter distance traveled than a lighter projectile.

## 4. How does the height of the incline affect the projectile's trajectory?

The height of the incline affects the projectile's trajectory by determining the initial potential energy of the projectile. The higher the incline, the greater the potential energy, resulting in a higher trajectory and a longer distance traveled.

## 5. Can a projectile roll down an incline instead of sliding?

Yes, a projectile can roll down an incline if it has a circular or spherical shape and is able to maintain its shape while rolling. In this case, the projectile's motion will be affected by both gravity and rotational motion, resulting in a unique trajectory down the incline.

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