Suppose a duck lives in a universe in which h=2πJ⋅sh=2πJ⋅s. The duck has a mass of 2.00 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the component of the duck’s velocity parallel to the pond’s width? (b) Assuming this uncertainty in speed prevails for 5.00 s, determine the uncertainty in the duck’s position after this time interval. a) The uncertainty principle is given as:hApAr >4TThe minimum uncertainty of the velocity is obtained for the maximumuncertainty of the position. Therefore:Ar = 1 mThus:hmAuAr =47hΔu=4TArm2т.Js> Au =4т 1m -2 kg> Au =|0.25 ms'b) If this uncertainty of velocity prevails for five seconds, we can simplyimagine that our position uncertainty grows for:Az' == Aut=|1.25 mTherefore our final uncertainty of position is:AX = Ar+ Ar> AX =2.25 m

uncertainty in position is given by ∆p∆x=h4πm∆v∆x=h4π=2πJs4π∆x=12m∆xJs∆x=0.25ms-1

Suppose a duck lives in a universe in which h=2πJ⋅s h=2πJ⋅s. The duck has a mass of 2.00 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the component of the duck’s velocity parallel to the pond’s width? (b) Assuming this uncertainty in speed prevails for 5.00 s, determine the uncertainty in the duck’s position after this time interval.