A 6.8 kg Cannonball is flying at 15.8 m/s [E] when it explodes into two fragments. One 1.4kg fragments (A) Goes off at 8.1 m/s [510 S of E]. What will be the magnitude of the velocity of the second fragment (B) immediately after the explosion? Assume that no mass was lost during the explosion.
To find the magnitude of the velocity of the second fragment (B) after the explosion, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system. Mathematically, it can be expressed as:
Total momentum before = Total momentum after
To apply this principle to the given scenario, we consider that the initial momentum before the explosion consists only of the cannonball's momentum. The final momentum after the explosion consists of the momentum of fragment A and fragment B.
Step 1: Calculate the initial momentum of the system.
The initial momentum of the system is given by the product of the mass and velocity of the cannonball:
Initial momentum before explosion = mass of cannonball * velocity of cannonball
Initial momentum before explosion = 6.8 kg * 15.8 m/s [E]
Step 2: Calculate the final momentum after the explosion.
The final momentum after the explosion is the sum of the momentum of fragment A and fragment B. Since we are looking for the magnitude of the velocity of fragment B, let's denote its velocity as v_b.
Final momentum after explosion = momentum of fragment A + momentum of fragment B
Final momentum after explosion = mass of fragment A * velocity of fragment A + mass of fragment B * velocity of fragment B
Given that mass of fragment A = 1.4 kg and velocity of fragment A = 8.1 m/s [510 S of E], we can substitute these values into the momentum equation:
0 = 1.4 kg * 8.1 m/s [510 S of E] + mass of fragment B * velocity of fragment B
Step 3: Solve for the magnitude of the velocity of fragment B.
Now we need to solve the equation to find the magnitude of the velocity of fragment B. Rearranging the equation, we can isolate the velocity of fragment B:
mass of fragment B * velocity of fragment B = -1.4 kg * 8.1 m/s [510 S of E]
Divide both sides by the mass of fragment B to solve for velocity:
velocity of fragment B = (-1.4 kg * 8.1 m/s [510 S of E]) / mass of fragment B
Since mass of fragment B is not given in the question, it is impossible to determine the magnitude of the velocity of fragment B without this information.