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Answer :
The final velocity of the two objects traveling together after the collision, determined by the conservation of momentum, is 5.78 m/s.
The student's question involves a collision where two objects with different masses and velocities collide and then travel together at a single velocity. As no external forces are acting on the system, we can use the conservation of momentum to find the final velocity of the combined mass. The formula to use here is:
Momentum before collision = Momentum after collision
(mA imes vA) + (mB imes vB) = (mA + mB) imes vfinal
Plugging in the provided values:
(5.00 kg imes 8.00 m/s) + (4.00 kg imes 3.00 m/s) = (5.00 kg + 4.00 kg) imes vfinal
(40.00 kg imes m/s) + (12.00 kg imes m/s) = 9.00 kg imes vfinal
52.00 kg imes m/s = 9.00 kg imes vfinal
Dividing both sides by 9.00 kg gives us:
vfinal = 5.78 m/s
Therefore, the final velocity of the two objects when they travel together after the collision is 5.78 m/s.
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