We need to calculate the speed of the bullet based on the information given:

Key Information:

• The distance between the two disks is $d = 67 \, \text{cm} = 0.67 \, \text{m}$.
• The angular displacement between the bullet holes is $\theta = 24.6^\circ = \frac{24.6}{360} \, \text{revolutions}$.
• The rotational speed of the disks is $f = 1350 \, \text{rev/min}$.

Steps to Solve:

1. Convert angular displacement to time: The angular displacement corresponds to the time it took for the bullet to travel the distance between the disks. The time can be calculated using the rotational speed: $t = \frac{\text{angular displacement}}{\text{rotational speed}}.$ Converting $1350 \, \text{rev/min}$ to revolutions per second ($\text{rev/s}$): $f = \frac{1350}{60} = 22.5 \, \text{rev/s}.$ Therefore, the time is: $t = \frac{\theta}{f} = \frac{\frac{24.6}{360}}{22.5}.$

2. Calculate the bullet speed: The speed of the bullet is given by: $v = \frac{d}{t}.$

Let me calculate this step-by-step. Given data distance_m = 0.67 # distance between disks in meters angular_displacement_deg = 24.6 # angular displacement in degrees rotational_speed_rpm = 1350 # rotational speed in revolutions per minute

Convert angular displacement to revolutions

angular_displacement_rev = angular_displacement_deg / 360

Convert rotational speed to revolutions per second

rotational_speed_rps = rotational_speed_rpm / 60

Calculate time (t = angular displacement / rotational speed)

time_s = angular_displacement_rev / rotational_speed_rps

Calculate bullet speed (v = d / t)

bullet_speed_m_s = distance_m / time_s

bullet_speed_m_sThe speed of the bullet is approximately 220.61 m/s.

Explanation:

1. The angular displacement of $24.6^\circ$ corresponds to the time it takes for the disks to rotate through that angle, given their rotational speed.
2. Using the time and the distance between the disks, the speed of the bullet is calculated.

Would you like me to elaborate further or solve related problems? Here are 5 related questions:

1. How does changing the rotational speed affect the accuracy of the measurement?
2. What is the time taken by the bullet to travel the 67 cm distance?
3. If the angular displacement were doubled, what would happen to the calculated speed of the bullet?
4. How would the result change if the distance between the disks was increased to 1 meter?
5. How can we improve the precision of such an experiment?

Tip: Always convert units to SI (meters, seconds) to avoid confusion in calculations!