Final answer:
After analyzing the points (10, 10), (-14, 10), and (20, 7), it is apparent that the ball's trajectory would pass through (0, 3), due to the symmetric nature of a parabolic path in projectile motion.
Step-by-step explanation:
To determine if a ball will pass through a specific point (0, 3) when following a parabolic path, we can use the information given by the points through which the ball passes: (10, 10), (-14, 10), and (20, 7). In physics, the trajectory of a projectile is typically parabolic and symmetric with respect to its vertex. When we look at the given points, we notice that the points (10, 10) and (-14, 10) are both at the same height (y-coordinate). This suggests that they could be equidistant from the vertex of the parabola on a horizontal line, and since their x-coordinates are different, the vertex should theoretically be at x = 0, halfway between these two points. However, to pass through the center at (0, 3), the vertex must not only be at x = 0 but also have a y-coordinate less than 10.
Given the symmetry and the fact that (10, 10) and (-14, 10) are at the same height, it is likely that the vertex of the parabola is below y = 10. Since the vertex would be the highest point of the parabola in a projectile motion scenario, and point (20, 7) provides additional confirmation of the downward concavity past the vertex, it stands to reason that the ball would indeed pass through the point (0, 3), which is lower than the height of the other two symmetric points (10, 10) and (-14, 10). Thus, the answer is Yes, the ball will pass through the center at (0, 3).