Calculating Building Height with Free Fall Kinematics | Spider-Man Example

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Homework Help Overview

The problem involves calculating the height of a building using free fall kinematics, specifically focusing on the distance Spider-Man falls in the last second of his descent. The original poster presents a scenario where Spider-Man falls a distance of h/4 in the final second of his fall, seeking to determine the total height h.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various kinematic equations and their applications to the problem, with some expressing uncertainty about their attempts and results. Questions are raised about the equations used and their effectiveness in solving for h.

Discussion Status

Several participants have shared their approaches, with one suggesting a focus on the time of fall and proposing specific equations to relate distance and time. While some participants have arrived at numerical answers, there is no explicit consensus on the correctness of these solutions, and the discussion continues to explore different interpretations and methods.

Contextual Notes

Participants note the complexity of the problem and the potential for multiple valid approaches, as well as the importance of correctly applying kinematic equations. There is an indication of varying levels of understanding among participants regarding the setup and assumptions of the problem.

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Homework Statement


Spider-Man steps from the top of a tall building. He falls freely from rest to the ground a distance of h. He falls a distance of h/4 in the last 1 second of his fall. What is h?


Homework Equations


All kinematic equations with free fall.


The Attempt at a Solution


I separated the motion into 2 cases where there was one part three times higher than the other. I made a bunch of equations that lead to nothing. Apparently I don't understand this.
 
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Which equations did you make? How do they lead to nothing?
 
Is it 276m?

What I did:

Let l = h/4

The Kinematics equation s = vit + 1/2 *at2

-l=v3l(1s) - 5*(1)2

gives (5-l) = v3

The distance spiderman moves before this is 3l, so using

vf2=vi2+2as

Vi is 0 since he starts from rest

so (5-l)^2=2*3*g*l

gives the quadratic equation l2-70x+25=0

Solving gives x = 0.358984 or 69.641

Multiply by 4 to get h.

I'm not sure if it's right though :rolleyes:
 
I made a bunch of equations that lead to nothing.

I think you just need the right 2 equations.

Focus on the time to fall. It falls 3/4 of the way in T1.

3/4*h = 1/2*g*T12

and

h = 1/2*g*T22

where T2 = T1 + 1

Solve for the total time and it's all down hill from there.
 
Thanks guys! That was a nice way to this problem LowlyPion. Also thanks physicsnoob93. I got 273m as my answer. I am pretty sure that's right after checking. Again thanks!
 
abhikesbhat said:
Thanks guys! That was a nice way to this problem LowlyPion. Also thanks physicsnoob93. I got 273m as my answer. I am pretty sure that's right after checking. Again thanks!
Not that it matters now, but I tried it both ways and they both give the same answer, 273m...
 

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