You have entered a contest in which the contestants drop a

Chapter 39, Problem 39.86

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You have entered a contest in which the contestants drop a marble with mass 20.0 g from the roof of a building onto a small target 25.0 m below. From uncertainty considerations, what is the typical distance by which you will miss the target, given that you aim with the highest possible precision? (Hint: The uncertainty xf in the x-coordinate of the marble when it reaches the ground comes in part from the uncertainty xi in the x-coordinate initially and in part from the initial uncertainty in vx. The latter gives rise to an uncertainty vx in the horizontal motion of the marble as it falls. The values of xi and vx are related by the uncertainty principle. A small xi gives rise to a large vx, and vice versa. Find the value of xi that gives the smallest total uncertainty in x at the ground. Ignore any effects of air resistance.)