Final answer:
The final velocity of the second ball after the collision is approximately 1.37 m/s at an angle of 146° with respect to the original line of motion.
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. The momentum of the first ball before the collision is given by its mass multiplied by its velocity, which is (5.60 m/s)(mass). The momentum of the second ball before the collision is zero because it is stationary. After the collision, the first ball moves at 4.64 m/s at an angle of 34° with respect to the original line of motion. To find the final velocity of the second ball, we can use the conservation of momentum formula: (mass of first ball)(velocity of first ball) + (mass of second ball)(velocity of second ball) = (mass of first ball)(final velocity of first ball) + (mass of second ball)(final velocity of second ball). Since the mass of the two balls is equal, we can simplify the equation to: (5.60 m/s)(mass) + 0 = (mass)(4.64 m/s cos(34°)) + (mass)(final velocity of the second ball). This allows us to solve for the final velocity of the second ball, which is: final velocity of second ball = (5.60 m/s)(mass) - (mass)(4.64 m/s cos(34°))/(mass). We can simplify further to the final velocity of the second ball = 5.60 m/s - 4.64 m/s cos(34°). The magnitude of this velocity is approximately 1.37 m/s. The direction of the second ball's velocity is given by the angle at which it moves with respect to the original line of motion. Since the first ball moves at an angle of 34° with respect to the original line of motion, the final velocity of the second ball will be at an angle of 180° - 34° = 146° with respect to the original line of motion.