Final answer:
The final velocity of the 25 kg object after the collision, when the 15 kg object continues to move to the left at 0.30 m/s, is -0.3 m/s. When the 15 kg object rebounds to the right at 0.45 m/s after the collision, the final velocity of the 25 kg object is 0.45 m/s. When the 15 kg object sticks together with the 25 kg object, the final velocity of the 25 kg object is -6.0 m/s.
Step-by-step explanation:
For this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system before a collision is equal to the total momentum after the collision.
(a) For the 25 kg object after the collision, we need to calculate the final velocity when the 15 kg object continues to move to the left at 0.30 m/s. Since momentum is conserved, we can set up the equation:
Initial momentum = Final momentum
(25 kg)(3.0 m/s) + (15 kg)(-6.0 m/s) = (25 kg + 15 kg)(v)
Solving for v, the final velocity of the 25 kg object is -0.3 m/s (moving to the left).
(b) When the 15 kg object rebounds to the right at 0.45 m/s after the collision, we can set up the equation:
(25 kg)(3.0 m/s) + (15 kg)(-6.0 m/s) = (25 kg + 15 kg)(v)
Using the same equation and solving for v, the final velocity of the 25 kg object is 0.45 m/s (moving to the right).
(c) When the 15 kg object sticks together with the 25 kg object, they will move as one object. Therefore, the final velocity of the 25 kg object will be the same as the initial velocity of the 15 kg object, but with the opposite sign. So, the final velocity would be -6.0 m/s (moving to the left).