# 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?

Sep 28, 2015

#### 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.

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

$+ \text{100 m} = {v}_{0} \cdot t + \frac{1}{2} \cdot \left(- g\right) \cdot {t}^{2}$

Positive displacement and negative gravitational acceleration.

• on the projectile's way down

$- \left(- \text{100 m}\right) = \frac{1}{2} \cdot g \cdot {t}^{2}$

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.