I have an online homework for my Modern Physics class, that requires me to find the uncertainty in velocity and position of a duck. The question is as below:
Suppose a duck lives in a universe in which h = 2π J · s. The duck has a mass of 2.55 kg and is initially known to be within a pond 1.70 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 4.10 s, determine the uncertainty in the duck's position after this time interval.
Now, I got the solution to the first part using the equation
$$ \Delta(x).\Delta(p) = h / 4\pi $$
This gives me $$ \Delta(v) > 0.1153$$
I assume, the second part of the question would be calculated this way:
$$\Delta(x) = \Delta(v) . t$$ or, $$ \Delta(x) = 0.1153 * 4.10$$
But this shows up as the wrong answer. What am I doing wrong? Wouldn't the uncertainty in the duck's position after time t equal the product of velocity uncertainty and time?
(Disclaimer: Yes, this is a homework question as I mentioned above, but I have tried to solve it and seem to be hitting a wall. I suppose I have some concept wrong. A nudge in the right direction would be appreciated.)