
Concept explainers
(a)
The minimum average distance by which the target was missed.
(a)

Answer to Problem 40P
The minimum average miss distance is
Explanation of Solution
The initial height of the pellet is
Write the given expression for deviation from the target
Here,
Write the uncertainty relation.
Here,
Substitute (I) and rearrange
Write the expression for change in velocity using equation of motion
Here,
Substitute
Write the expression for time taken to reach distance
Substitute (IV) and (II) in (I)
Find the uncertainty in initial position by differentiating the above equation with respect to
Since the second derivative of equation (V) is positive. The above found
Rearrange for
Conclusion
Substitute
Thus, the minimum average miss distance is
(b)
Find the average miss distance given the mass and height.
(b)

Answer to Problem 40P
The average miss distance is
Explanation of Solution
The mass of the pellet is
Substitute
Thus, the average miss distance is
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