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

[abhikesbhat]

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.

 

[diazona]

Which equations did you make? How do they lead to nothing?

 

[physicsnoob93]

Is it 276m?

What I did:

Let l = h/4

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

-l=v_3l(1s) - 5*(1)²

gives (5-l) = v₃

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

v_f²=v_i2+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

 

[LowlyPion]

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.

 

[abhikesbhat]

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!

 

[diazona]

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...