Final answer:
To find the velocity of the second ball in a billiard ball collision, conservation of momentum and energy principles are used to solve for the vertical and horizontal velocity components. The velocity magnitude and direction are then calculated from these components.
Step-by-step explanation:
The student's question involves a collision between two billiard balls where one is initially stationary and the other one is moving. To solve for the velocity of the second ball after the collision, we can apply the principles of conservation of momentum and conservation of kinetic energy since the collision is elastic. Since both balls have the same mass and one is stationary before the collision, the velocity of the first ball after the collision can be used to determine the velocity of the second ball after the collision.
Using the given information of the first ball's velocity before and after the collision, and the angle at which it travels after collision, we can decompose the movement into horizontal and vertical components and apply the conservation laws to find out the components of the velocity of the second ball. The resulting velocity (magnitude and direction) can then be calculated with the Pythagorean theorem and trigonometry.