Question

For projectile motion, for example if i set my coordinate system as positive so that means that the acceleration and the max height (dy) is going to be positive?

Answer 1

Here's how you can think about this.

Explanation:

Now, let's say that you launch a projectile straight up and that it reaches a maximum height of 100 meters.

You can break down its movement into two parts

• moving up towards maximum height
• falling from maximum height

If you take the upward direction to be positive and the ground level to be sero, then the displacement of the projectile will be

• positive on its way up, since it goes from ground level to 100m in the assigned positive direction;
• negative on its way down, since now it is moving from 100m to ground level;

What about the gravitational acceleration? You know that gravity is always pulling objects towards the ground. If the upward direction remains the positive direction, then `g` will be

• negative while the projectile moves towards maximum height, i.e. as it climbs, since `g` is a vector directed towards the surface of the Earth and the projectile is moving in the opposite direction;
• positive while the projectile is falling from maximum height, since now the direction of gravity is the same as the direction of the projectile.

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So, in this example, if you take `v_0` to be the initial velocity of the projectile, you can say that

• on the projectile's way up

`+"100 m" = v_0 * t + 1/2 * (-g) * t^2`

Positive displacement and negative gravitational acceleration.

• on the projectile's way down

`-(-"100 m") = 1/2 * g * t^2`

Negative displacement and positive gravitational acceleration.

So remember, `g` is positive if the motion of the object has the same direction as the direction of the gravitational acceleration vector, `vec(g)`, and negative if it has the opposite direction.