Final answer:
In an elastic collision between two balls with equal mass and given velocities, the final velocity of mass one can be determined using the principle of conservation of momentum.
Step-by-step explanation:
In an elastic collision between two balls with equal mass, both momentum and kinetic energy are conserved. To find the velocity of mass one after the collision, we can use the principle of conservation of momentum.
Before the collision, mass one has a velocity of 1.0 m/s to the right, which is positive, and mass two has a velocity of 2.0 m/s to the left, which is negative.
Using the conservation of momentum equation: (mass one velocity * mass one mass) + (mass two velocity * mass two mass) = (mass one final velocity * mass one mass) + (mass two final velocity * mass two mass), we can solve for the final velocity of mass one.
Plugging in the known values, the final velocity of mass one is -1.5 m/s, which is answer choice a.