Question

Imagine a small child whose legs are half as long as her parent’s legs. If her parent can walk at maximum speed V, at what maximum speed can the child walk?

Answer 1

`\boxed{v=\frac {V}{\sqrt {2}}}`

Step-by-step explanation:

We know that speed is given by dividing distance by time or multiplying length and frequency. The speed of the father will be given by Lf where L is the length of the father’s leg ad f is the frequency.

We know that frequency of simple pendulum follows that
`f=\frac {1}{2\pi} \sqrt {\frac {g}{l}}`

Now, the speed of the father will be
`V=Lf= L* (\frac {1}{2\pi} \sqrt {\frac {g}{l}})` while for the child the speed will be
`v=\frac {L}{2}* (\frac {1}{2\pi} \sqrt {\frac {g}{0.5l}})`

The ratio of the father’s speed to the child’s speed will be

`\frac {V}{v}=\frac {\frac {L}{2}* (\frac {1}{2\pi} \sqrt {\frac {g}{0.5l}})}{ L* (\frac {1}{2\pi} \sqrt {\frac {g}{l}})}\\\frac {V}{v}=\frac {\sqrt {2}}{2}\\\boxed{v=\frac {V}{\sqrt {2}}}`