Final answer:
By applying the law of conservation of momentum to both spheres and then comparing the kinetic energy before and after the collision, we can find the final velocity of the 1.50 kg sphere and determine the type of collision (elastic or inelastic).
Step-by-step explanation:
To determine the final velocity of the 1.50 kg sphere after the collision, we can use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. We'll work on vector components. The initial momentum of the system is the sum of the momenta of both spheres: 0.500 kg * (2.00i - 2.90j + 1.00k) m/s, 1.50 kg * (-1.00i + 2.00j - 2.50k) m/s. After the collision, we know the velocity of the 0.500 kg sphere, so we can calculate its momentum and then deduce the momentum, and hence the velocity, of the 1.50 kg sphere. To identify the kind of collision, we must determine if the kinetic energy is conserved. By calculating the kinetic energy before and after the collision for both spheres and comparing them, we can tell if it is an elastic or inelastic collision.