A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing the principles of Vertical displacement data projectile motion, the soldier decides to perform a simple experiment at the indoor firing range. The soldier hangs a target a distance of d = 114 m from the end of the barrel. The rifle is Bullet drop h in cm mounted so that the bullet exits moving horizontally at the same height as the bull's-eye. After 6.03 six trials, the soldier tabulates the values they measured for the distance h from the bull's-eye to 7.34 the bullet strike. 7.36 5.94 d 7.16 5.96 What is the most accurate muzzle velocity vm that the soldier can report to their sergeant? Um = 982 m/s What is the uncertainty ơp in this measurement?

College Physics
11th Edition
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing the principles of projectile motion, the soldier decides to perform a simple experiment at the indoor firing range. The soldier hangs a target a distance of \( d = 114 \, \text{m} \) from the end of the barrel. The rifle is mounted so that the bullet exits moving horizontally at the same height as the bull's-eye. After six trials, the soldier tabulates the values they measured for the distance \( h \) from the bull's-eye to the bullet strike.

**Diagram Explanation:**
- The diagram shows a rifle aimed horizontally with the bullet trajectory represented by a dashed line.
- The target is marked with a bull's-eye, and the vertical distance \( h \) from the trajectory to the bull's-eye is indicated.
- The horizontal distance \( d \) from the rifle to the target is marked.

**Vertical Displacement Data Table:**
- The table shows the bullet drop \( h \) in centimeters for six trials:

| Bullet drop \( h \) in cm |
|---------------------------|
| 6.03                       |
| 7.34                       |
| 7.36                       |
| 5.94                       |
| 7.16                       |
| 5.96                       |

**Calculation of Muzzle Velocity:**
- The most accurate muzzle velocity \( v_m \) that the soldier can report to their sergeant is given as:

\[
v_m = 982 \, \text{m/s}
\]

**Uncertainty in Measurement:**
- The problem asks: What is the uncertainty \( \sigma_{v_m} \) in this measurement?

(Note: The assignment does not provide the uncertainty value, so it remains unspecified in this transcription.)
Transcribed Image Text:A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing the principles of projectile motion, the soldier decides to perform a simple experiment at the indoor firing range. The soldier hangs a target a distance of \( d = 114 \, \text{m} \) from the end of the barrel. The rifle is mounted so that the bullet exits moving horizontally at the same height as the bull's-eye. After six trials, the soldier tabulates the values they measured for the distance \( h \) from the bull's-eye to the bullet strike. **Diagram Explanation:** - The diagram shows a rifle aimed horizontally with the bullet trajectory represented by a dashed line. - The target is marked with a bull's-eye, and the vertical distance \( h \) from the trajectory to the bull's-eye is indicated. - The horizontal distance \( d \) from the rifle to the target is marked. **Vertical Displacement Data Table:** - The table shows the bullet drop \( h \) in centimeters for six trials: | Bullet drop \( h \) in cm | |---------------------------| | 6.03 | | 7.34 | | 7.36 | | 5.94 | | 7.16 | | 5.96 | **Calculation of Muzzle Velocity:** - The most accurate muzzle velocity \( v_m \) that the soldier can report to their sergeant is given as: \[ v_m = 982 \, \text{m/s} \] **Uncertainty in Measurement:** - The problem asks: What is the uncertainty \( \sigma_{v_m} \) in this measurement? (Note: The assignment does not provide the uncertainty value, so it remains unspecified in this transcription.)
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