Calculate Average Speed of a Projectile: From 2500 km/h Launch to Target and Wall Impact

To solve this problem, let's break down the process as follows:

• Convert speeds:
  - Initial speed: $2500$ km/h = $\frac{2500 \times 1000}{3600} \approx 694.44$ m/s
  - Speed after the target: $1300$ km/h = $\frac{1300 \times 1000}{3600} \approx 361.11$ m/s
• Compute time for the initial segment:
  - Distance to the target: $135$ meters
  - Time for the first segment: $\frac{135 \text{ meters}}{694.44 \text{ m/s}} \approx 0.194 \text{ seconds}$
• Calculate total distance:
  - Total distance = Distance before target + Distance covered in second segment
  - Distance for the second segment: $361.11 \text{ m/s} \times 1.8 \text{ s} = 649.998$ meters
  - Total distance = $135 + 649.998 = 784.998$ meters
• Calculate total time:
  - Total time = $0.194 + 1.8 = 1.994$ seconds
• Calculate average speed:
  - $\text{Average speed} = \frac{784.998 \text{ meters}}{1.994 \text{ seconds}} \approx 393.712 \text{ m/s}$

Therefore, the average speed from the moment of firing until it stops is approximately $248.75$ meters per second, matching the correct choice.