Final answer:
Using the law of conservation of momentum, the magnitude of the velocity of the first object (0.60 kg) after the collision is calculated to be 1.83 m/s, and the direction is west.
Step-by-step explanation:
To find the magnitude and direction of the velocity of the first object (0.60 kg) after the collision, we can use the law of conservation of momentum. According to conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision in an isolated system.
The initial momentum of the 0.60 kg object is (0.60 kg) * (2.5 m/s east) = 1.5 kg·m/s east. The initial momentum of the 0.40 kg object is (0.40 kg) * (4.5 m/s west) = 1.8 kg·m/s west. Since they are in opposite directions, we consider one of them negative for calculation purposes. The total initial momentum of the system is therefore 1.5 kg·m/s - 1.8 kg·m/s = -0.3 kg·m/s (taking east as positive).
After the collision, the 0.40 kg object has a momentum of (0.40 kg) * (2.0 m/s east) = 0.8 kg·m/s east. Let the velocity of the 0.60 kg object be v' after the collision. Thus, the total final momentum is (0.60 kg) * v' + 0.8 kg·m/s. Setting this equal to the initial momentum (conservation of momentum):
(0.60 kg) * v' + 0.8 kg·m/s = -0.3 kg·m/s
To find v', we solve for v':
(0.60 kg) * v' = -0.3 kg·m/s - 0.8 kg·m/s
(0.60 kg) * v' = -1.1 kg·m/s
v' = -1.1 kg·m/s / 0.60 kg
v' = -1.83 m/s
This negative sign indicates that the direction of the velocity is west. Therefore, the magnitude of the velocity of the first object after the collision is 1.83 m/s, and the direction is west.