How Do You Derive the Initial Vertical Velocity Equation?

[Aquaticus]

Hi can anyone help me with this formula:

How do I end up with this equation, thanks in advance!

 

[PeterO]

Hi can anyone help me with this formula: View attachment 38940

How do I end up with this equation, thanks in advance!

It looks like a re-arrangement of one of the 5 standard equations of motion under constant acceleration - which is what you get during vertical motion near the Earths surface [constant acceleration that is]

EDIT: Though given the symbols used, it looks like there is an error in the transformation - but without the symbols being defined you can't be certain.

 

[Aquaticus]

Can I use it to determine the maximum initial velocity?

 

[PeterO]

Can I use it to determine the maximum initial velocity?

How would you propose to do that?

 

[Aquaticus]

I don't know, I'm really stuck on that maximum initial velocity part

 

[PeterO]

I don't know, I'm really stuck on that maximum initial velocity part

maximum initial velocity was not part of your original post. What actual question are you trying to solve?

 

[Aquaticus]

The question I want to solve is:

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

It is classified as a hard question which got me thinking...

I think that assumptions are a key role here, at the same time I have seen many other equations on how to solve for the initial velocity - but not the maximum.

 

[PeterO]

The question I want to solve is:

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

It is classified as a hard question which got me thinking...

I think that assumptions are a key role here, at the same time I have seen many other equations on how to solve for the initial velocity - but not the maximum.

I answered that question in another thread - look around.

 

[Aquaticus]

Is it really that simple? Doesn't it have to do with some trigonometric functions?

 

[PeterO]

Is it really that simple? Doesn't it have to do with some trigonometric functions?

It is that simple - made so by the words "estimate" and "you".

 

[Aquaticus]

What do you mean by "you"?

(Does your answer involve the maximum initial velocity?)

 

[PeterO]

What do you mean by "you"?

(Does your answer involve the maximum initial velocity?)

The original question was

Estimate the "maximum velocity" you can throw a standard Tennis Ball.

 

[Aquaticus]

Why do you think this question s classified as hard? Might it be that one should make assumptions? Or what do you think?

 

[PeterO]

Why do you think this question s classified as hard? Might it be that one should make assumptions? Or what do you think?

It is hard because you are not just plugging numbers into a formula. You have to realistically estimate what you yourself can do.
Since you are throwing a tennis ball, the ball is quite irrelevant as your arm if far heavier than the ball.
It would be interesting to turn up to call in an upper body cast, and offer the answer 0.1 m/s.

Another classic example is to hang masses of 100g, 200g, 300g, etc on the end of a spring, and note that it extends say 5cm, 10cm then 15 cm.
The question is then posed: what if we hang 250kg on the spring.
Some people suggest 125 m, which follows the nature of the spring, but ignores the fact that the spring is probably made of only 1 metre of wire, coiled up, so is unlikely to become 125 m long.

 

[Aquaticus]

What is the vertical motion formulae?