How Fast Does a Ball Fall 25 Feet: Physics & Algebra Answer

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Discussion Overview

The discussion revolves around calculating the time and velocity of a ball falling from a height of 25 feet using physics and algebra. Participants explore the relationship between distance, time, and velocity, addressing both the mathematical and conceptual aspects of the problem.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the formula d = 16t^2 to calculate the distance fallen in feet.
  • Another participant calculates time as t = √(25/16) but notes that velocity at that time still needs to be determined.
  • There is a claim that the answer for time is 1 1/4 or 5/4, with a request for validation of this calculation.
  • One participant emphasizes that the derived time is not the velocity and asks for the velocity function.
  • A suggestion is made that finding the first derivative of distance with respect to time would yield a velocity formula, but there is confusion regarding whether acceleration is constant.
  • Another participant asserts that the acceleration is constant and corrects the derivative expression to reflect this assumption.
  • There is skepticism about the participants' understanding of basic calculus and arithmetic, particularly regarding the derivative and the calculation of 2*16.
  • A different approach is presented using the equation d = ut + 1/2 at^2, leading to a comparison with the original formula and questioning the nature of the ball's fall.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to finding velocity and whether the acceleration is constant. There is no consensus on the final calculations or the understanding of the underlying physics principles.

Contextual Notes

Some participants appear to have misunderstandings about the mathematical steps involved, particularly in deriving velocity from distance. There is also ambiguity regarding the conditions of the ball's fall, such as whether it is in free fall.

Joseph
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What is the answer to how fast a ball fall's form 25 feet useing the formula d = 16t2 :confused:
 
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[tex]d = 16t^2[/tex]

I assume that this gives the distance in feet. So,

[tex]t = \sqrt{25/16}[/tex]

However you want the velocity of the ball at t = that number above. Can you finish now?
 
physics and algebra

I think the answer is 1 1/4 or 5/4 can you tell me if i am on the right track.? :rolleyes:
 
Yes, that is correct.
 
This is only the time, not the velocity at that time. You still need to find velocity as a function of time. Can you do that?
 
if you find the first derivative of distance as a function of time this wud give you a formula for velocity if acceleration is not constant, in this case it wud be
d'(t) = 36t.
 
FUNKER said:
if you find the first derivative of distance as a function of time this wud give you a formula for velocity if acceleration is not constant, in this case it wud be
d'(t) = 36t.


Judging by the title, I don't think Joseph would know calculus. However, I could be wrong.
 
FUNKER said:
if you find the first derivative of distance as a function of time this wud give you a formula for velocity if acceleration is not constant, in this case it wud be
d'(t) = 36t.
Eh. . . The acceleration is constant. your post should read: "If you find the first derivative of distance as a function of time this would give you a formula for velocity, in this case it would be d'(t) = 36t."
 
The_Brain said:
Judging by the title, I don't think Joseph would know calculus. However, I could be wrong.

Froget calculus; judging by this, "d'(t) = 36t" and the number of times it's been quoted in the last few posts, I don't think anyone here knows what 2*16 is!
 
  • #10
hey,
d = u*t + 1/2 a*t2
=> 25 = 1/2 g*t2 ......(1)
but according to the question
d = 16 t2
or
25 = 16t2.......(2)

comparing (1) and (2)
1/2g=16

g= 32 feet/ second squared ??

or 12.8 metres/second squared ??

was the ball really undergoing a free fall ??
 

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