# Ball dropped in air at 20m/s, why v=20 not v0=20

1. Dec 12, 2016

### MrGoATi

1. The problem statement, all variables and given/known data
ball dropped in air at 20m/s.
why is v=20,v0=0 instead of v0=20,v=0

2. Relevant equations
a=v-v0 / t
s=x0+v0xt + at2/2

3. The attempt at a solution
a=g=9.8m/s2

I know I can solve it with first finding time(I get that) a=v-v0/t making it into t=v-v0/g
so 20/9.8=2.04s
but now from what I understand 20m/s is v0 is it not? can someone explain is it or is it not initial velocity, and why we don't use
s=v0xt+ gt2/2

I know the answer is 20.4m, or maybe it's actually wrong?

Last edited: Dec 12, 2016
2. Dec 12, 2016

### Staff: Mentor

Can you please supply the exact problem statement.

3. Dec 12, 2016

### MrGoATi

the task is to find maximum height,

but i'm pretty sure it's 20.4 I am asking about whether velocity is v0 or v . and how do I know which is it in tasks I may have in future.

4. Dec 12, 2016

### TomHart

vo typically means initial velocity, and v (or vf) typically means final velocity. But what is not clear to me is what is happening in this problem. You say that the ball is "dropped in air at 20 m/s". That statement itself is confusing. Add to it that you are trying to find maximum height. Is it the case that the ball is being thrown upward from the ground at 20 m/s? If that is true, then the initial velocity (vo) would be 20 m/s, and the final velocity (velocity at maximum height, that is) would be 0 m/s.

Welcome to Physics Forums.

5. Dec 12, 2016

### MrGoATi

yeah exactly but from a ton of forums I watched solutions to this they use
s=v0xt+ gt2/2
but end up with s=gt2/2
finding that a ball thrown up with 20m/s will get to ground to maximum height in 2.04s, 20.4m
the task is quite easy, but since it is so confusing for me that v0=0 I think I will be just as confused in exams when I see anything else than this with velocities and acceleration.

6. Dec 12, 2016

### TomHart

If the equation reduces to s=gt2/2, that would be for a problem where the initial velocity was 0. That is why the vot term went away - as would be the case if a ball was dropped off of a building - dropped meaning that it started with an initial velocity (vo) of 0 m/s.

7. Dec 12, 2016

### PeroK

Suppose a ball is thrown upwards at initial speed $v _0$ and reaches its maximum height, $s$ at $t_1$ seconds. Then:

$t_1 = \frac{v_0}{g}$, hence $v_0 = gt_1$

And:

$s = v_0 t_1 - \frac{1}{2}{g}t_1^2$

Now, substituting $v_0 = gt_1$ into this equation gives:

$s = gt_1^2 - \frac{1}{2}{g}t_1^2 = \frac{1}{2}{g}t_1^2$

8. Dec 12, 2016

### MrGoATi

thanks, now i get it. explains a lot

9. Dec 12, 2016

### TomHart

Me too.

10. Dec 12, 2016

### Staff: Mentor

MrGoATi: If you had provided the exact problem statement like I asked, this confusion could have been avoided. Please, in the future, provide the complete problem statement, and not your own interpretation.

11. Dec 12, 2016

### MrGoATi

i did completely state all that was given, and when you asked i answered what i needed to find. thanks for suggestion though i will keep that in mind

12. Dec 12, 2016

### Staff: Mentor

What you stated was not the exact statement of the problem as it was originally written. It was your paraphrasing of the problem statement.

13. Dec 12, 2016

### MrGoATi

[ post: 5642023, member: 345636"]What you stated was not the exact statement of the problem as it was originally written. It was your paraphrasing of the problem statement.[/QUOTE]
,,ball dropped in air at 20m/s.,, that's the given information the question was ,maximum height, which i told when you asked. i could not tell you exact statement since it is written in Lithuanian. but there's no more info. it's nine word task.

14. Dec 12, 2016

### Staff: Mentor

,,ball dropped in air at 20m/s.,, that's the given information the question was ,maximum height, which i told when you asked. i could not tell you exact statement since it is written in Lithuanian. but there's no more info. it's nine word task.[/QUOTE]
Yikes. Whoever stated the problem for you in that way did you a great disservice. They should be berated. I hope this doesn't always happen.

Chet