Suppose a duck lives in a universe in which h 2 J s The du

Suppose a duck lives in a universe in which h = 2 J · s. The duck has a mass of 2.85 kg and is initially known to be within a pond 1.20 m wide.

(a) What is the minimum uncertainty in the component of the duck\'s velocity parallel to the pond\'s width?
u m/s

(b) Assuming this uncertainty in speed prevails for 5.90 s, determine the uncertainty in the duck\'s position after this time interval.
m

Solution

According to the Uncertainty Principle:
x*p > /2

= h/2

Since h = 2J*s,
= h/2 = 2J*s / 2 = 1 J*s

Thus the Uncertainty Principle in Fuzzy\'s Universe is:
x*p > 1/2 J*s

a)
From the initial conditions:
x = 1.20 m
p = mv = 2.85kg * v

Given:
x*p > 1/2 J*s
1.20 m * 2.85kg * v > 1/2 J*s
v > 1/2 J*s / (1.20 m * 2.85kg)
v > 0.1461 m/s

b)
x*p > 1/2 J*s
p = m*v = 2.85kg * 0.1461 m/s = 0.416 m*kg/s
x > 1/2 J*s / p
x > 1/2 J*s / 0.416 m*kg/s
x > 1.21 m