Maya, a high school student in physics, is analyzing a projectile launched at 30 m/s at a 30° angle. If the acceleration due to gravity is \(9.8 \, \text{m/s}^2\), what is the maximum height reached by the projectile?

["### How High Does Maya’s Projectile Go? Analyzing Maximum Height in Physics", "Physics invites students like Maya to explore real-world motion through equations — and nothing brings physics to life like projectile motion. Maya, a bright high school student, recently launched a projectile with precision: 30 m/s at a 30° angle. Understanding the maximum height it reaches offers a perfect blend of trigonometry and kinematics.", "#### The Physics Behind Maximum Height", "When a projectile is launched at an angle, its motion can be broken into horizontal and vertical components. The vertical motion determines how high the projectile climbs before descending. Gravity acts downward with acceleration ( g = 9.8 , \ ext{m/s}^2 ), slowing the upward velocity until it momentarily stops — this peak height is the goal.", "Maya’s launch speed is 30 m/s at 30° above the horizontal. To find maximum height, we focus solely on the vertical component of velocity.", "#### Step 1: Resolve the initial velocity", "The vertical component of velocity ( v_{y} ) is found using:\n[\nv_y = v \cdot \sin(\ heta)\n]\nwhere ( v = 30 , \ ext{m/s} ) and ( \ heta = 30^\circ ).\nSince ( \sin(30^\circ) = 0.5 ),\n[\nv_y = 30 \ imes 0.5 = 15 , \ ext{m/s}\n]", "#### Step 2: Use kinematic equation to find maximum height", "At maximum height, the vertical velocity becomes zero (( v = 0 )), and acceleration is ( -9.8 , \ ext{m/s}^2 ) (negative because it opposes upward motion). Using:\n[\nv^2 = u^2 + 2as\n]\nwith ( v = 0 ), ( u = 15 , \ ext{m/s} ), ( a = -9.8 , \ ext{m/s}^2 ), solve for ( s ) (height):\n[\n0 = (15)^2 + 2(-9.8)s\n]\n[\n0 = 225 - 19.6s\n]\n[\n19.6s = 225\n]\n[\ns = \frac{225}{19.6} \approx 11.48 , \ ext{meters}\n]", "#### Conclusion: Maya’s Projectile Reaches ≈ 11.5 m", "Thus, Maya’s projectile climbs to a maximum height of approximately 11.5 meters — a clear victory of physics in action. Whether for a science fair or exam, analyzing projectile motion reinforces key concepts in kinematics and problem-solving.", "By mastering equations like ( v^2 = u^2 + 2as ) and carefully resolving vectors, students unlock deeper understanding — just like Maya did.", "Keywords: projectile motion physics, Maya high school student, maximum height calculation, kinematics second quarter, high school physics problem, gravity acceleration 9.8 m/s², velocity components, vertical motion, physics projectile analysis."]