B

To analyze the maximum heights attained by the three balls, we need to consider the factors that influence the height of a projectile. The maximum height $h$ reached by an object projected vertically is given by the equation:
$$h = \frac{v^2}{2g}$$
where $v$ is the initial velocity and $g$ is the acceleration due to gravity.
Assuming that the balls are projected with the same initial velocity but at different angles (15°, 45°, and 75°), we can reason as follows:

• The angle of 45° provides the optimal angle for maximum range and height, giving it an advantage over the other angles.
• For angles less than 45° (like 15°), the vertical component of the initial velocity is lower compared to the angle of 45°.
• For angles greater than 45° (like 75°), the vertical component is again reduced because most of the initial velocity goes into height rather than range, resulting in a lower height than at 45°.

Therefore, the order of maximum heights attained will be:
$$h_{15} < h_{45} < h_{75}$$.
Hence, the correct option is B: h 15 < h 45 < h 75.