Final answer:
The situation involves a collision where one must apply the conservation of momentum to find the final velocity of the bowling ball. The question of whether the collision is elastic is answered by comparing kinetic energies before and after the event. Spin could potentially convert rotational kinetic energy to linear kinetic energy during the collision.
Step-by-step explanation:
Understanding Momentum and Collision
When a 5.50-kg bowling ball moving at 9.00 m/s collides with a 0.850-kg bowling pin that ends up moving at 15.0 m/s at a 15.8° angle, we can analyze the situation using the principles of conservation of momentum and possibly conservation of kinetic energy, depending on whether the collision is elastic or inelastic.
To answer the first part of the question, we would need to use the conservation of linear momentum since it is conserved in all collisions. To determine the final velocity of the bowling ball, one would apply the conservation of momentum in two dimensions since the pin scatters at an angle. Vector components of momentum before and after the collision would be equated — horizontal components and vertical components separately — to solve for the missing velocity components of the bowling ball. After finding the components, one would use the Pythagorean theorem to find the magnitude and trigonometry to find the direction.
For the question about the collision being elastic, one would compare the total kinetic energy before and after the collision. If the kinetic energy is conserved, the collision is elastic; if not, it's inelastic. The spin of a bowling ball could affect the outcome of the collision as it could translate some rotational kinetic energy into linear kinetic energy.