Final answer:
In a conservation of momentum scenario within Physics, the total momentum before the collision is conserved after the collision. For the collision of the submarine sandwich and grilled cheese sandwich on a frictionless surface, the final velocity of the system is calculated to be 0.775 m/s to the left.
Step-by-step explanation:
The question involves a conservation of momentum scenario in Physics, specifically analyzing the outcome of a collision between two objects with known masses and velocities. For objects involving frictionless surfaces and straight-line movement, the conservation of momentum dictates that the total momentum of the system before collision is equal to the total momentum of the system after the collision.
To find the final velocity of the system after the collision of the submarine sandwich and the grilled cheese sandwich, we use the formula:
Total Momentum before collision = Total Momentum after collision
(m1 \u00d7 v1) + (m2 \u00d7 v2) = (m1 + m2) \u00d7 Vfinal
Where m1 and m2 are the masses of the two sandwiches, v1 and v2 are their respective velocities, and Vfinal is the velocity of the combined mass after the collision.
Using the values provided for the submarine sandwich (0.550 kg moving 3.05 m/s to the left) and the grilled cheese sandwich (0.250 kg moving 1.25 m/s to the right), and considering left as the negative direction and right as the positive direction, we get:
(0.550 kg \u00d7 -3.05 m/s) + (0.250 kg \u00d7 1.25 m/s) = (0.550 kg + 0.250 kg) \u00d7 Vfinal
After performing the calculation, we find that the final velocity of the combined mass after the collision is 0.775 m/s to the left, making option (a) the correct answer.