Why must vertical acceleration always be negative on projectile motion?

  • #1
[tex] y= y_0 + v_(y0)t - 1/2gt^2 [/tex]

why is it -1/2 gt^2???
what if somebody was to throw ball downward?
is that still negative velocity?


wait, does negative in velocity mean direction?? or slowing down
kind of confused while writing this question
if it is direction why is it negative for throwing the ball upward?
 

Answers and Replies

  • #2
461
8
[tex] y= y_0 + v_(y0)t - 1/2gt^2 [/tex]

why is it -1/2 gt^2???
what if somebody was to throw ball downward?
is that still negative velocity?


wait, does negative in velocity mean direction?? or slowing down
kind of confused while writing this question
if it is direction why is it negative for throwing the ball upward?
The signs are only due to your choice in coordinates. You can chose different coordinates and make your acceleration positive.The ones you use now are just the least awkward for this situation.Try to flip or rotate your coordinates and get the equations describing parabolic motion. The physics is the same the equations are not.
 
  • #3
Pengwuino
Gold Member
4,989
16
As bp_psy stated, it is a matter of what your coordinate system convention is.

If you decide "up" is positive, then the acceleration is always negative (since it points down towards what is typically the Earth in these projectile motion problems). If the projectile is moving upwards, the velocity is positive; if it is moving downwards, the velocity is negative. If you decide "up" is negative, the acceleration is always positive because it points down and will have opposite sign. If the projectile is moving up, the velocity is negative; if it is moving downward, the velocity is positive.

The idea of "slowing down" and "speeding up" is kind of vague. The positive/negative sign on the velocity or acceleration doesn't tell you if the object is speeding up or slowing down alone. For example, if you throw a ball upwards, the acceleration points downward and at the beginning you could say it is slowing down. However, after it reaches the top, comes to rest, and begins falling again, you could then say it's speeding up! What "speeding up/slowing down" really refers to is the magnitude of the velocity (in other words, what the velocity is regardless of the sign).
 
  • #4
sophiecentaur
Science Advisor
Gold Member
2020 Award
25,384
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You can use any sign you like but you need to be consistent, once you have made the choice. Slowing down on the way up is the same (-g) as speeding up as you are dropping downwards because the sign for direction is different for up and down.
You just need to let the Maths do the work for you and interpret the answer that comes out of the other end correctly. It can't let you down.
 

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