How Do You Derive the Initial Vertical Velocity Equation?

In summary, the conversation is discussing how to solve for the maximum initial velocity of a regular tennis ball. The original question is to estimate the maximum velocity that can be achieved with a regular tennis ball, but the conversation also touches on the difficulty of this question and the assumptions that need to be made. It is suggested that it is a re-arrangement of one of the 5 standard equations of motion under constant acceleration, but there may be an error in the transformation. The conversation also mentions using trigonometric functions and assumptions to solve for the initial velocity. Overall, the conversation is focused on solving the problem and discussing the various factors and approaches involved.
  • #1
Aquaticus
22
0
Hi can anyone help me with this formula:
vertical_displacement_equation_initial_velocity.png


How do I end up with this equation, thanks in advance!
 
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  • #2
Aquaticus said:
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.
 
  • #3
Can I use it to determine the maximum initial velocity?
 
  • #4
Aquaticus said:
Can I use it to determine the maximum initial velocity?

How would you propose to do that?
 
  • #5
I don't know, I'm really stuck on that maximum initial velocity part
 
  • #6
Aquaticus said:
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?
 
  • #7
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.
 
  • #8
Aquaticus said:
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.
 
  • #9
Is it really that simple? Doesn't it have to do with some trigonometric functions?
 
  • #10
Aquaticus said:
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".
 
  • #11
What do you mean by "you"?

(Does your answer involve the maximum initial velocity?)
 
  • #12
Aquaticus said:
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.
 
  • #13
Why do you think this question s classified as hard? Might it be that one should make assumptions? Or what do you think?
 
  • #14
Aquaticus said:
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.
 
  • #15
What is the vertical motion formulae?
 

1. What is initial vertical velocity?

Initial vertical velocity is the velocity at which an object is thrown or launched into the air in a vertical direction.

2. How is initial vertical velocity calculated?

Initial vertical velocity can be calculated by dividing the change in vertical position by the change in time, or by using the equation v0y = vfy - gt, where v0y is the initial vertical velocity, vfy is the final vertical velocity, g is the acceleration due to gravity, and t is the time.

3. What factors affect initial vertical velocity?

The factors that affect initial vertical velocity include the force applied to the object, the angle at which the object is thrown or launched, and the mass and shape of the object.

4. Why is initial vertical velocity important in physics?

Initial vertical velocity is important in physics because it helps determine the motion of objects in free fall or projectile motion. It is also used in calculations to determine the height, time, and distance of an object's motion.

5. Can initial vertical velocity be negative?

Yes, initial vertical velocity can be negative if the object is thrown or launched downward. In this case, the acceleration due to gravity will also be negative, and the object will be moving in the opposite direction of the positive vertical axis.

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