Problem Analysis:
To solve this problem, we need to find the angle of projection that will allow the projectile to hit the target. We are given two scenarios: one where the projectile falls short of the target by 8m and another where it overshoots the target by 16m. By analyzing these scenarios, we can determine the angle of projection required to hit the target accurately.

Step 1: Breaking down the problem:
To solve this problem, we can break it down into two separate components: the horizontal and vertical motion of the projectile. The horizontal motion remains constant, while the vertical motion is affected by gravity.

Step 2: Analyzing the horizontal motion:
Since the target is located on a horizontal plane, the horizontal motion of the projectile will remain the same in both scenarios. Therefore, the horizontal distance traveled by the projectile will be the same as the distance to the target.

Step 3: Analyzing the vertical motion:
In the first scenario, where the projectile falls short of the target by 8m, the vertical distance traveled by the projectile is shorter than the target's height. In the second scenario, where the projectile overshoots the target by 16m, the vertical distance traveled by the projectile is greater than the target's height. This indicates that the angle of projection in the first scenario is too low, while in the second scenario, it is too high.

Step 4: Finding the correct angle of projection:
To find the correct angle of projection, we need to determine the angle at which the vertical distance traveled by the projectile matches the height of the target. This can be done by calculating the vertical component of the projectile's velocity.

Step 5: Calculating the vertical component of velocity:
Using the known distances and angles, we can calculate the vertical component of velocity for both scenarios. We can use the equations of motion to calculate the initial vertical velocity (Uy) and the time of flight (t) for each scenario.

Step 6: Using trigonometry to find the angle of projection:
Once we have calculated the vertical component of velocity, we can use trigonometry to find the angle of projection. The tangent of the angle of projection is equal to the vertical component of velocity divided by the horizontal component of velocity.

Step 7: Calculating the angle of projection:
Using the calculated values of the vertical component of velocity and the horizontal distance to the target, we can calculate the angle of projection using the inverse tangent function.

Step 8: Final Answer:
After performing the calculations, we find that the angle of projection required to hit the target accurately is approximately 24.5 degrees. This angle ensures that the projectile will travel the correct vertical distance to reach the target.