Maximum Initial Velocity of a Tennis Ball: Solving for the Optimal Launch Speed

[Aquaticus]

Hi there all, I'm new to this forum and I really need some help. The question is described as follows:

Estimate the maximum "initial velocity" that you can achieve with a regular tennis ball.

Presumably there are no variables, nor are there any equations involved.

I think that an assumption would be necessary, but how do I solve it? I should also say that this is marked as a "hard question".

I would really appreciate if someone helped me, thanks in advance!

 

[PeterO]

Hi there all, I'm new to this forum and I really need some help. The question is described as follows:

Estimate the maximum "initial velocity" that you can achieve with a regular tennis ball.

Presumably there are no variables, nor are there any equations involved.

I think that an assumption would be necessary, but how do I solve it? I should also say that this is marked as a "hard question".

I would really appreciate if someone helped me, thanks in advance!

Are you allowed to use a tennis racket or a baseball bat or similar, or are you just throwing it/kicking it?

 

[Aquaticus]

I'm just throwing it.

 

[PeterO]

I'm just throwing it.

Fine. Not sure how big you are, but when I throw something, my hand moves about 1m. I can manage to move it that far in perhaps 1/4 second. That would mean it averages 4 m/s.
If I have managed to accelerate my hand uniformly all that time, the final speed will be twice the average speed so that would mean 8m/s tops for me [and I am not sure I can actually move my hand that fast].
Note that a standard tennis ball is not heavy enough to slow my hand too much. now had it been a shot-put I would have been in trouble.

Note also: If I manage to throw it at 10m/s, it means I could throw it 5m into the air if I threw it straight up. Not sure I can throw that high??

 

[Aquaticus]

I have to show it with algebra, how can I do that?

 

[PeterO]

I have to show it with algebra, how can I do that?

To quote the lead character from a great Australian movie - The Castle - "Tell 'em they're dreaming!"

But if you want some algebra, you could use the maximum range formula
Maximum Range = v² / g

You could estimate how far you can possibly throw a tennis ball for the range, and use g=10 since it is only an approximation only.

Alternately you could estimate/claim how far you can throw a tennis ball straight up, and use the vertical motion formulae to calculate an initial velocity.

Note: be reasonable in your estimates.
I reckon I could throw a tennis ball to the other end of a tennis court - I wonder how long they are? I could maybe throw from base to base on a baseball diamond too?
I reckon I could perhaps throw a ball to 8m straight up, but I am tall so I would be releasing the ball about 2m from the ground for a start

 

[Aquaticus]

Isn't there any derivation involved (it has to do with the maximum initial velocity)?