Does v^2=v_0^2-2gh work if the positive axis is up and the initial velocity is down? In the situation where the positive axis is up, the acceleration due to gravity is g, and the velocity is represented by the equation v2=v_0^2−2gh. This works great if the initial velocity is upwards. But say, what if the initial velocity is downwards?. While we all know intuitively that the acceleration due to gravity would increase the speed (and thus v^2 would increase), this equation says that the speed (and thus v^2) would decrease. How is this justified?

cousinhaui

cousinhaui

Answered question

2022-10-28

Does v 2 = v 0 2 2 g h work if the positive axis is up and the initial velocity is down?
In the situation where the positive axis is up, the acceleration due to gravity is g, and the velocity is represented by the equation v 2 = v 0 2 2 g h. This works great if the initial velocity is upwards. But say, what if the initial velocity is downwards?. While we all know intuitively that the acceleration due to gravity would increase the speed (and thus v 2 would increase), this equation says that the speed (and thus v 2 ) would decrease. How is this justified?

Answer & Explanation

scapatofc

scapatofc

Beginner2022-10-29Added 12 answers

You are looking at a specific application of a more general formula
v q 2 v o q 2 = 2 a q ( q q o ) ,
where
q is the coordinate direction,
the v terms are velocity components along the q axis,
a q is the constant acceleration component along the q axis,
and q and q o are the positions along the q axis, which match, respectively with v q and v o q
For constant acceleration along the q axis between locations q and q o , this always works, regardless of the signs of v q and v o q (because both of those get squared). You must pay attention to the sign of the acceleration and the signs of the positions.
Kasey Reese

Kasey Reese

Beginner2022-10-30Added 3 answers

It doesn't say that. If the positive axis is "up" as you put it, when the initial velocity is "downwards" that means that h is always negative, meaning the -2gh term goes positive.

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