Answer :
Final answer:
The recoil speed of a 346 kg cannon that fires a 12 kg cannonball at a speed of 126 m/s is approximately 4.4 m/s, determined by the conservation of momentum.
Explanation:
The subject of the student's question is Physics, specifically dealing with the conservation of momentum. When a cannon fires a cannonball, the momentum before and after the event must remain constant assuming no external forces are acting on the system. Therefore, to calculate the recoil speed of the cannon, we'll use the formula derived from the conservation of momentum:
mcannon * vcannon recoil = mcannonball * vcannonball
According to the question, the mass of the cannon (mcannon) is 346 kg and the cannonball (mcannonball) is 12 kg traveling at the speed (vcannonball) of 126 m/s. Solving for the recoil speed of the cannon (vcannon recoil), we get:
vcannon recoil = (mcannonball * vcannonball) / mcannon
vcannon recoil = (12 kg * 126 m/s) / 346 kg
vcannon recoil = 1512 m/s2 / 346 kg
vcannon recoil = 4.37 m/s
Rounding to two significant figures, the recoil speed of the cannon is approximately 4.4 m/s, which corresponds to option (b).
