D

Step 1: Understanding the Range of Projectiles
The range of a projectile launched at an angle \( \theta \) with an initial speed \( v_0 \) is given by the formula:
\[ R = \frac{v_0^2 \sin(2\theta)}{g} \]
where \( g \) is the acceleration due to gravity.

Step 2: Calculating the Ranges
Let's calculate the ranges for angles 15°, 45°, and 75°:
- For \( \theta = 15° \):
\[ R_{15} = \frac{v_0^2 \sin(30°)}{g} = \frac{v_0^2 \cdot 0.5}{g} = \frac{0.5 v_0^2}{g} \]

- For \( \theta = 45° \):
\[ R_{45} = \frac{v_0^2 \sin(90°)}{g} = \frac{v_0^2}{g} \]

- For \( \theta = 75° \):
\[ R_{75} = \frac{v_0^2 \sin(150°)}{g} = \frac{v_0^2 imes 0.5}{g} = \frac{0.5 v_0^2}{g} \]

Step 3: Comparing the Ranges
From the calculations, we see that:
\[ R_{15} = \frac{0.5 v_0^2}{g} < R_{45} = \frac{v_0^2}{g} > R_{75} = \frac{0.5 v_0^2}{g} \]
Therefore, we have:
\[ R_{15} = R_{75} < R_{45} \]

Step 4: Conclusion
Thus, the ranges can be ranked as follows:
\[ R_{15} = R_{75} < R_{45} \]
Therefore, the correct answer is: R 15 = R 75 < R 45.