Answer :
Final answer:
The collision of the two balls is governed by the principle of conservation of momentum. Initial and final momentum are equal and opposite. When calculated, the total final velocity of the balls is -2.29 m/s, which means they're moving leftwards.
Explanation:
This question is connected with the principle of conservation of momentum. In a collision, the total momentum before the collision is equal to the total momentum after the collision, provided no external forces are acting on the system.
Here, the 3.00 kg ball is moving rightwards (which we'll take as the positive direction) and the 4.00 kg ball is moving to the left (negative direction). Their initial momenta are (3.00 kg * 8.00 m/s) and (-4.00 kg * 10 m/s). So the total initial momentum is (24 kg*m/s - 40 kg*m/s) = -16 kg*m/s.
After the collision, the two balls stick together forming a single object of mass (3.00 kg + 4.00 kg) = 7.00 kg. It will move with a velocity we'll denote as 'v'.
Given the conservation of momentum, we have: Initial momentum = final momentum, so -16 kg*m/s = 7.00 kg * v. Solving for 'v' gives us v = -16 kg*m/s / 7.00 kg = -2.29 m/s. The negative sign indicates that the balls are moving leftwards after collision.
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