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?

1 Answer
Sep 28, 2015

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.

http://everythingmaths.co.za/science/grade-12/03-vertical-projectile-motion/03-vertical-projectile-motion-02.cnxmlplus

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.