Bungee Jump

[harpazo]

In bungee jumping, a bungee jump is the amount the cord will stretch at the bottom of the fall. The stiffness of the cord is related to the amount of stretch by the equation given below.

K = [(2W(S+L)]/(S^2)

W= weight

K = cord stiffness (pounds per foot)

L = free length of cord (feet)

S = stretch (feet)

(a) A 180-pound person plans to jump off a ledge attached to a cord of length 57 feet. If the stiffness of the cord is no less than 22 pounds per foot, how much will the cord stretch?

Solution:

W = 180
L = 57
K = 22

I now plug and chug, right?

(b) If safety requirements will not permit the jumper to get any closer than 3 feet to the ground, what is the minimum height required for the ledge in part (a)?

I need help for part (b). I just want the set up. Do I need to find L?

 

[Otis]

In bungee jumping, a bungee jump is the amount the cord will stretch ...

S = stretch (feet)

A bungee jump is S? That's an odd definition for a bungee jump. Please check, to make sure you copied the exercise correctly.

When a person bungee jumps, they dive head-first from a structure with the cord attached to their legs. In other words, if the cord were stretched all the way with a person hanging upside down by their legs (not moving), then the top of their head would be closer to the ground than the end of the cord because the stretched length of the cord (S+L) is measured from the top of the structure only to their legs, not to the top of their head.

It doesn't even make sense to define the jump's distance as S.

Maybe it's poor wording and we're supposed to assume the length of the stretched cord includes the jumper's entire body-length. (Silly.)

... stiffness ... is no less than 22 pounds per foot,

how much will the cord stretch? ...

Note that it says, "no less than 22". That means 22 or more (an inequality). So, they're really asking, "At most, how much will the cord stretch". (S gets larger as K gets smaller, and 22 is the smallest value of K.)

The answer to part (a) takes the form: S ≤ value

W=180 L=57 K=22
I now plug and chug, right?

Yes, assuming the 57 feet of cord (plus the additional stretch S) includes the length of the jumper's body. After you substitute for W,L,K, you'll have a quadratic equation. The positive solution gives the largest value of S.

... what is the minimum height required for the [structure] ... Do I need to find L?

No, you don't need to find L because they already gave it to you. L is 57.

You need to use both L and the maximum value of S found in part (a). The minimum distance from the structure to the ground has two parts: the 3-foot buffer and the stretched length of the cord (which includes the jumper's body length).

PS: You typed K = [(2W(S+L)]/(S^2)

That has mismatched parentheses, and we don't need the square brackets.

K = (2W)(S+L)/S^2

?

 

[harpazo]

Thanks. I copied and pasted the question as found online.

Is the set up for part (a) as follows:

57 = (2•180)(s + 22)/(s^2) ?

 

[Otis]

... I copied and pasted the question as found online.

What web site is that?

Is the set up for part (a) as follows:

57 = (2•180)(s + 22)/(s^2) ?

Almost. Double-check the substitutions.

After you correct the mistake, multiply each side of the equation by S^2. (We cannot solve for a variable, as long as it appears in a denominator. Multiplying by the denominator will clear the algebraic fraction.)

It's a quadratic equation; you know what to do next.

PS: The variable is S, not s.

?

 

[harpazo]

What web site is that?


Almost. Double-check the substitutions.

After you correct the mistake, multiply each side of the equation by S^2. (We cannot solve for a variable, as long as it appears in a denominator. Multiplying by the denominator will clear the algebraic fraction.)

It's a quadratic equation; you know what to do next.

PS: The variable is S, not s.

?

I went to Wolfram and this is what the S value turned out to be:

Wolfram|Alpha: Making the world’s knowledge computable

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

m.wolframalpha.com

 

[Otis]

I went to Wolfram and this is what the [positive] S value turned out to be ...

Instead of posting a link to a pair of numerical expressions located in the middle of a calculator page, it would be more helpful (for readers) to simply type the number asked for in part (a).

S ≤ 39.8

It's a word problem, so we could answer with a complete sentence (including units): The cord will stretch no more than 39.8 ft.

Are you working on part (b)?

?

 

[harpazo]

S ≤ 39.8

How did you get 39.8 feet?
Can you provide the equation set up for part (b)? I will do the math work.

 

[Otis]

How did you get 39.8 feet?

I looked at your solutions (I mean wolframalpha's solutions, as you asked a machine to do your work), and I evaluated each of those expressions -- to get decimal approximations. After that, I ignored the negative solution and rounded the other (arbitrarily) to the nearest tenth of a foot.

Have you forgotten how to evaluate numerical expressions? (Use the Order of Operations.)

Or, maybe you forgot why you were trying to solve the quadratic in the first place. Do you know what symbol S represents?

I just don't understand what you're doing here, harpazo. I will not provide an equation for part (b). I want you to draw a picture and think about what part (b) is talking about. If we simply spoon feed you, I'm concerned that you'll never be able to stand on your own feet.

?

 

[harpazo]

I want you to draw a picture and think about what part (b) is talking about. If we simply spoon feed you, I'm concerned that you'll never be able to stand on your own feet.

Ok. I will continue working to solve part (b).

 

[harpazo]

Ok. I will continue working to solve part (b).

S = stretch of cord at the bottom of the fall.