Aman walks at$\mathbf{1}\mathit{m}\mathbf{/}\mathit{s}$, known to within an uncertainty (unrealistically small) of$\mathbf{\text{1}}\mathbf{}\mathit{\mu }\mathbf{\text{m/h}}$.

(a) Compare the minimum uncertainty in his position to his actual physical dimension in his direction of motion $\mathbf{25}\mathit{c}\mathit{m}$,from front to back.

(b) Is it sensible to apply the uncertainty principle to the man?

The position and speed of particles (like electron and photon) is not known with perfect accuracy. This is the principle of Uncertainty.

Man weight$65kg$

Speed$1m/s$

Uncertainty$\text{1}\mu \text{m/h}$

Given the uncertainty in the velocityv, we need to figure out the position measurement$\text{(}\Delta \text{x)}$constraint.

$$\begin{gathered} \Delta \text{p}\Delta \text{x}⩾\frac{h}{2} \\ \text{m}\Delta \text{v}\Delta \text{x}⩾\frac{h}{2} \\ 65kg\times \frac{{\displaystyle {\text{10}}^{\text{- 6}}}}{{\displaystyle \text{3600}}}m/s\times \Delta \text{x≥}\frac{{\displaystyle {\text{1.054×10}}^{\text{- 34}}\frac{kg\times {\displaystyle {{\displaystyle \text{m}}}^{\text{2}}}}{s}}}{{\displaystyle \text{2}}} \\ \Delta \text{x≥}\frac{{\displaystyle {\text{1.054×10}}^{\text{-34}}\text{m}}}{2\times {\displaystyle {{\displaystyle \text{1.81×10}}}^{\text{- 8}}}} \\ \Delta {\text{x≥2.91×10}}^{\text{- 27}}\text{m} \\ \Delta \text{x}~{\text{10}}^{-26}\text{×}25\text{cm} \end{gathered}$$

Hence the solution is $\Delta \text{x}~{\text{10}}^{-26}\times 25\text{cm}$

The ambiguity in position is around ${\text{10}}^{\text{- 26}}$ orders of magnitude smaller than the man's width. Beyond the experimental observations, this is a very small value; therefore applying the uncertainty relation is pointless. The answer is No,it is not sensible to apply the uncertainty principle to the man.