A marksman fires a practice round from A toward a target B....

A marksman fires a practice round from $A$ toward a target $B$. If the target diameter is $160 \mathrm{mm}$ and the target center is at the same altitude as the end of the rifle barrel, determine the range of "shallow" launch angles $\theta$ for which the round will strike the target. Neglect aerodynamic drag and assume that the round is directed along the vertical centerline of the target. (Note: The word "shallow" indicates a low-flying trajectory for the round.

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Key Concepts

Target Intersection Analysis

This concept pertains to determining the conditions under which the projectile's path will intersect a given target area. It involves calculating the range of launch angles that ensure the vertical position of the projectile at the target's horizontal location falls within the target's dimensions, accounting for the target’s size and position.

Parabolic Trajectory

A projectile follows a parabolic path when only gravitational forces act on it after being launched. Understanding the shape and properties of this trajectory is critical to determine when and where the projectile will be at a specific horizontal distance.

Kinematic Equations

These are the mathematical relationships that describe the motion of the projectile. They include formulas for displacement, velocity, and time in both the horizontal and vertical directions, which are essential for determining the position of the projectile at any given time.

Projectile Motion

This key concept involves the analysis of an object’s motion under the influence of gravity only, neglecting air resistance. The motion is decomposed into horizontal and vertical components, each of which can be analyzed independently using constant acceleration equations in the vertical direction and constant velocity in the horizontal direction.

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