Proportional ratios with exponents - Need Help

[kathleenhelen]

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!

 

[tiny-tim]

welcome to pf!

hi kathleenhelen! welcome to pf!

v ∝ L/T. If the period is measured to be proportional to Lp, where p = 4/5

that doesn't make sense

do you mean the period is measured to be proportional to L^4/5 ?

 

[kathleenhelen]

Yes! Sorry, I mistyped the question by accident, but the 4/5 is supposed to be an exponent.

 

[tiny-tim]

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 = bL^4/5 for some constant b

so v = … ? ​