Final answer:
The final velocity of the second ball after the collision is found using the conservation of momentum, with the given initial velocities and the final velocity of the first ball. The magnitude of the final velocity vector and the angle is then calculated to get the speed and directional angle of the second ball.
Step-by-step explanation:
The student's question pertains to finding the final velocity of the second ball after a collision between two balls with masses m and 2m, given the initial velocities and the final velocity of the first ball. To solve this, we'll use the principle of conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act on it.
The initial momentum of the system can be expressed as:
Pi = m×vi,1 + 2m×vi,2
Substituting the given values, we have:
Pi = m×(12i - 5j) + 2m×(-3i + 2j)
The final momentum of the system must equal the initial momentum and can be written as:
Pf = m×vf,1 + 2m×vf,2
Using the given final velocity of the first ball (8i + 7j), we can solve for the final velocity of the second ball:
vf,2 = × (Pi - m×vf,1) / 2m
By plugging in the values and simplifying, we find the final velocity of the second ball in (i, j, k) notation.
To find the speed and angle of the second ball's final velocity, we calculate the magnitude of the velocity vector and use trigonometry to find the angle relative to a chosen axis, typically the x-axis.