I have a few doubts on how the acceleration of a ball works when we throw it up in the air, In my mind, I could imagine it in some different "real world" cases, So I am listing them all down, though I suspect the same reasoning would apply to all.
- Say I jump out of my building's terrace (don't worry, I believe I can fly :D) and then Mid-way down, I throw a tennis ball up/down, in both cases, the instant after the ball leaves my hand, How does the acceleration of the ball compare to $g$ (ie. $>$ or $<$ or $=$)
- Say I am jumping on a trampoline and while going up, I throw the ball up/down, the instant after the ball leaves my hand, How does the acceleration of the ball compare to $g$ (ie. $>$ or $<$ or $=$)
- Say I am standing still and I throw the ball up, the instant after the ball leaves my hand, How does the acceleration of the ball compare to $g$ (ie. $>$ or $<$ or $=$)
In all of these, we are assuming there is no wind/ air friction etc. and that $g$ (gravitaional acceleration) is a fixed constant $(=-9.8)$ everywhere near Earth, so like $100 m$ up or down isn't affecting $g$
So, I was doing HRK, when 2 questions came up that were essentially asking the exact same things I am asking in case 1.
My thoughts: I thought that when I throw the ball up while falling down, the acceleration must be positive for an instant, or at least like $-9.8 + c$ (where $c$ is a positive number). My reasoning was as follows: If we throw the system onto a cartesian plane and direct up to be positive, then originally, the ball (and me) have a negative velocity, but when I throw the ball up, it has a positive velocity, which means there MUST have been an acceleration/Force. This was in agreement with the fact that in the book, when drawing the graph of a rebounding ball, they had shown a discontinuity in the acceleration, for the same reason I have described above. So, for a small instant the acceleration is $> -9.8$ but then comes back to $-9.8$ (which is what I am assuming $g$ is).
For the case when I am falling down and throwing the ball up, for a similar reason I thought that the acceleration at first must be $< -9.8$ and then come back to $-9.8$
As the Solutions to HRK's MCQ's are not given, I decided to check my answers from @knzhou 's answer key, and he stated that the Answer to both questions should be that acceleration is $-9.8$.
Now, I am $100$% sure that he must've been right (IPHO gold medallist orz), But I don't seem to understand the reason why...
About 15 months ago I had learned a little newtonian mechanics (without calculus) from an exam-prep like book, and after that, I hadn't looked at it for almost a year now, but now that I have started to learn Physics again, I want to really understand intuitively most of the things I can, So, this question may be a little elementary/ stupid, But I would still really appreciate if you could answer these.