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Chapter 2: Problem 202

Shooters \(\mathrm{A}\) and \(\mathrm{B}\) each shoot three arrows at their target, aiming for a bull's-eye. Which shooter is more precise? Which shooter is more accurate? Explain.

Short Answer

Expert verified
Shooter A is more precise due to smaller distances between arrows (more tightly grouped), indicating higher consistency. Shooter B is more accurate, as they have a smaller average distance from the bull's-eye, meaning they are closer to the target.

Step by step solution

01

Define precision and accuracy

Precision: Essentially, the grouping of the arrows. The closer the arrows are to each other, the higher the precision. Accuracy: The closeness of the arrows to the bull's-eye. If the arrows are closer to the bull's-eye, the shooter is considered more accurate.
02

Evaluate Shooter A's performance

Shooter A's performance would be given in terms of the distance between his/her three arrows and their average distance from the bull's-eye. For example, if shooter A's arrows' distances from the bull's-eye were as follows: Arrow 1: 5 cm Arrow 2: 6 cm Arrow 3: 5.5 cm Then, the average distance from the bull's-eye would be: \(\frac{5 + 6 + 5.5}{3} = 5.5 \textrm{ cm}\). To determine the precision, we look at the distance between the arrows. In this example, their distances are between 0.5 cm and 1 cm apart, which would indicate some level of precision.
03

Evaluate Shooter B's performance

Similar to step 2, Shooter B's performance would be given in terms of the distance between his/her three arrows and their average distance from the bull's-eye. For example, if shooter B's arrows' distances from the bull's-eye were as follows: Arrow 1: 3 cm Arrow 2: 7 cm Arrow 3: 4 cm Then, the average distance from the bull's-eye would be: \(\frac{3 + 7 + 4}{3} = 4.67 \textrm{ cm}\). To determine the precision, we look at the distance between the arrows. In this example, their distances are between 1 cm and 4 cm apart, which would indicate lower precision compared to Shooter A.
04

Compare and draw conclusions

Compare the average distances and the distances between arrows for each shooter. In our example: Shooter A: Average distance from bull's-eye = 5.5 cm; Distance between arrows = 0.5 cm - 1 cm Shooter B: Average distance from bull's-eye = 4.67 cm; Distance between arrows = 1 cm - 4 cm From these results, we can conclude that Shooter B is more accurate, as he/she has a smaller average distance from the bull's-eye. However, Shooter A is more precise, as the distances between his/her arrows are smaller (more tightly grouped) compared to Shooter B.

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Most popular questions from this chapter

(a) If \(25.0 \mathrm{~cm}^{3}\) of an unknown substance has a mass of \(195 \mathrm{~g}\), what is the density of the substance in grams per cubic centimeter? (b) How many cubic centimeters does \(500.0 \mathrm{~g}\) of the substance occupy? (c) Does this substance sink or float in mercury, which has a density of \(13.6 \mathrm{~g} / \mathrm{mL} ?\)

Explain what effect compressing a gas has on the density of the gas.

Do the following calculations and express each answer in scientific notation: (a) \(\left(5.03 \times 10^{2}\right)+\left(8.1 \times 10^{1}\right)\) (b) \(\left(8.32 \times 10^{-5}\right) \times\left(0.53 \times 10^{4}\right)\) (c) \(\frac{6.02 \times 10^{23}}{3}\), where the 3 is an exact number (d) \(\left(3.960 \times 10^{3}\right)-\left(4.62 \times 10^{2}\right)\)

Define density, and explain why the unit for density is called a derived SI unit.

(a) Solve the equation \(y=z / x\) for \(x\). (b) Solve the equation \(y=z / 2 x\) for \(x\).
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