Is the Faulty Velocity Equation for Projectile Launch Valid?

In summary, the conversation discusses an equation used to calculate the velocity of a projectile launched off a table top. The equation is D=√(g/2h), where D is the horizontal distance traveled, h is the table height, and g is the gravitational acceleration. The conversation also mentions the units of the expression and the difficulty in accurately measuring the time component. The validity of the equation is questioned, and the conversation ends with a discussion about the algebra and units involved in the equation.
  • #1
DAB
6
0
I have seen this equation used to calculate the velocity of a projectile being launched off a table top.
upload_2018-2-24_11-51-5.png
Where D=horizontal distance travelled, h=table height, and g=gravitational acceleration. Nowhere else can I find a calculation of velocity based on only two distances and GA. Everything I see has a time component or one of the velocity variables (V-i, V-f). Is this equation valid? It seems too simple. I don't care about exploring air resistance or drag coefficients, just a simple velocity at lauch calculation.
 

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  • #2
DAB said:
Everything I see has a time component
What are the units of ##\sqrt{g/2h}##
 
  • #3
D and h in meters, g= -9.8 m/sec squared
 
  • #4
So what are the units of ##\sqrt{g/2h}##
 
  • #5
I guess I'm not understanding your question. g is the GA constant of -9.8 meter/second squared and h is the height of the table. Do you want a measurement for h? One measurement I have for this is h= -1.25 meters and D= 2.4 meters. That's all the information that seems to be required to calculate V (velocity at launch).
 
  • #6
He is asking for the units of the expression. Here is a hint:

##\sqrt\frac{\Big(\frac{m}{s^2}\Big)}{m}##

When cancellations are done, what units do you have left?
 
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  • #7
The answer (V) is expressed in m/s. meters/second
 
  • #8
DAB said:
I have seen this equation used to calculate the velocity of a projectile being launched off a table top. View attachment 220987 Where D=horizontal distance travelled, h=table height, and g=gravitational acceleration. Nowhere else can I find a calculation of velocity based on only two distances and GA. Everything I see has a time component or one of the velocity variables (V-i, V-f). Is this equation valid? It seems too simple. I don't care about exploring air resistance or drag coefficients, just a simple velocity at lauch calculation.
Can you check whether the equation is true in an example case?
 
  • #9
How would I know for sure? I'd have to be able to measure the time and the time measurement would be so small that I'd not be able to accurately measure it. I guess I could quesstimate it, but it would be under a second, so pretty hard to measure accurately.
 
  • #10
DAB said:
How would I know for sure? I'd have to be able to measure the time and the time measurement would be so small that I'd not be able to accurately measure it. I guess I could quesstimate it, but it would be under a second, so pretty hard to measure accurately.

I meant try some ##v## and ##h##. Calculate ##D## and check the formula.

I assume your algebra isn't good enough to prove or disprove the general case. The next best thing is to try a few examples.
 
  • #11
This was a simple question. I just wanted to know if anyone had ever seen this equation before. It seems too simple to calculate velocity especially when other equations have one calculating both horizontal and vertical components to arrive at an answer.
Maybe you can answer one last question for me. Tell me if my algebra is correct in calculating that
upload_2018-2-24_11-51-5-png.png
is equal to
upload_2018-2-24_15-24-38.png
 

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  • #12
What people were hinting to earlier is that the units of the expression with the radical are ##\frac{1}{seconds}##. So that is the time aspect you were wondering about.

Specifically, the expression

##\sqrt\frac{2h}{g}##

is the time it takes an object to fall a distance h. So if D is the distance traveled horizontally when the object first touches the floor and this is divided by the travel time, we should get an expression for the horizontal velocity when the object left the table.
 
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  • #13
DAB said:
I guess I'm not understanding your question.
Apparently not. The quantity ##\sqrt{g/2h}## has units of ##1/s## in SI units. So in your OP when you said “Everything I see has a time component” it turns out that ##\sqrt{g/2h}## is the time component you are used to seeing.
 

Related to Is the Faulty Velocity Equation for Projectile Launch Valid?

1. What is a faulty velocity equation?

A faulty velocity equation is a mathematical formula that is used to calculate the velocity of an object, but it contains errors or is missing important variables, resulting in an incorrect calculation.

2. How can a faulty velocity equation affect scientific experiments?

A faulty velocity equation can lead to incorrect results in scientific experiments that involve the measurement of velocity. This can impact the validity and reliability of the data collected, and may lead to incorrect conclusions being drawn.

3. What are some common errors found in faulty velocity equations?

Common errors found in faulty velocity equations include incorrect units, missing or incorrect variables, and incorrect mathematical operations. These errors can occur due to human error or incorrect assumptions.

4. How can scientists identify and correct a faulty velocity equation?

Scientists can identify a faulty velocity equation by carefully examining the formula and checking for errors. They can also compare the results obtained from the equation with other known values. To correct the equation, scientists may need to consult with other experts or conduct further research to determine the correct variables and mathematical operations.

5. How can scientists prevent using a faulty velocity equation in their experiments?

To prevent using a faulty velocity equation, scientists should always double-check their equations and calculations before using them in experiments. They should also consult with other experts and conduct thorough research to ensure the accuracy of their equations.

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