Proportional ratios with exponents - Need Help

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Homework Help Overview

The problem involves the relationship between a walker's speed, leg length, and the period of leg motion, framed within the context of proportional ratios and exponents. The original poster seeks to determine the power of leg length to which speed is proportional, given that the period is proportional to leg length raised to the exponent 4/5.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster expresses confusion about how to approach the problem and requests detailed explanations. Some participants question the clarity of the proportionality statement regarding the period and suggest a possible typographical error. Others attempt to clarify the relationships between the variables involved.

Discussion Status

The discussion is ongoing, with participants exploring the relationships between speed, leg length, and period. Some guidance has been offered regarding the formulation of the relationships, but no consensus or resolution has been reached yet.

Contextual Notes

The original poster's confusion stems from the interpretation of the proportionality involving the exponent, which has led to a need for clarification on the definitions and relationships of the variables.

kathleenhelen
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proportional ratios with exponents - Need Help!

A walker's speed, v, is proportional to the ratio of his leg length, L, and the period of the repeating motion of his legs, T, that is, v ∝ L/T. If the period is measured to be proportional to Lp, where p = 4/5, what power of L must the speed be proportional to?



I have absolutely no idea how to do this problem. I've tried it a couple times and I'm getting no where with it. Please help! The more you could explain the answer the more helpful it would be as well!
 
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welcome to pf!

hi kathleenhelen! welcome to pf! :smile:
kathleenhelen said:
v ∝ L/T. If the period is measured to be proportional to Lp, where p = 4/5

that doesn't make sense :confused:

do you mean the period is measured to be proportional to L4/5 ?
 


Yes! Sorry, I mistyped the question by accident, but the 4/5 is supposed to be an exponent.
 
kathleenhelen said:
A walker's speed, v, is proportional to the ratio of his leg length, L, and the period of the repeating motion of his legs, T, that is, v ∝ L/T. If the period is measured to be proportional to Lp, where p = 4/5, what power of L must the speed be proportional to?

ok, v ∝ L/T means v = aL/T for some constant a

similarly T = bL4/5 for some constant b

so v = … ? :smile:​
 

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