Proportional ratios with exponents - Need Help

AI Thread Summary
The discussion focuses on determining the proportional relationship between a walker's speed, leg length, and the period of leg motion. The speed, v, is given as proportional to the ratio of leg length, L, and the period, T, expressed as v ∝ L/T. The period is specified to be proportional to L raised to the power of 4/5, leading to T ∝ L^(4/5). By substituting this relationship into the speed equation, the participants aim to find the power of L that the speed must be proportional to. The conversation emphasizes the need for clarity in mathematical expressions and the correct application of proportional relationships.
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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