# Kinematic sign convention

For example, if I drop a ball from a $50$ meters building, then I will consider

1. the ground is $0$ meter

2. downward is positive ( which makes gravity positive, downward velocity positive, etc)

so with that if i use $X_f = X_i + V_it + \frac{1}{2}at^2$ then I would get something like $0 = 50 + 4.9t^2$ which is not even possible.

Instinctively I know what to do but when I think more about sign convention, it seems so confusing.

• Please use Math Notation for readability. Commented Aug 21, 2014 at 22:59
• If positive is downwards then initial velocity or initial height has to be negative. Are you shooting downwards or upwards? Commented Aug 21, 2014 at 23:00
• you need to use a consistent sign convention for direction, velocity and acceleration... Commented Aug 21, 2014 at 23:23

You want $X_i=-50$. The ground is zero, down is positive, so the top of the building is at $-50$. There's no universal convention. You're stuck figuring it out from scratch each time. Fortunately once you do it several times you'll get the hang of it.

• There is a convention that makes gravity potential negative, and thus moving towards the center of the earth is towards negative. Commented Aug 21, 2014 at 23:02

If you say that the acceleration of gravity is towards the ground and positive, then you must have distance increasing in that direction as well - so top of building is zero, and ground is 50. In that case

$$y(t) = y(0) + v_0t + \frac12gt^2\\ 50 = 0 + 4.9 t^2$$

Or you say that the vertical direction is "up is positive"; then the acceleration of gravity is negative. Then the top of the building is at 50, the ground is at 0, and

$$y(t) = y(0) + v_0t + \frac12gt^2\\ 0 = 50 - 4.9 t^2$$

Or if you want the ground to be zero, and downwards is positive, then the top of the roof is at -50 and

$$0 = -50 + 4.9 t^2$$

Whichever you choose, as long as you are consistent in your conventions all is well.

• I can't say the ground is 0 if I pick downward is positive? Commented Aug 22, 2014 at 0:09
• You can - but then the top of the roof must be negative. See my updated answer. Commented Aug 22, 2014 at 0:12
• Ah I get it now, thankyou so much! Commented Aug 22, 2014 at 0:17