A projectile is launched from the ground with an initial velocity of 50 m/s at an angle of 30 degrees above the horizontal. Ignoring air resistance, calculate the maximum height reached by the projectile.
["# Projectile Motion: Maximum Height Calculated for a 50 m/s Launch at 30° Angle", "When a projectile is launched from the ground with an initial speed and angle, its motion follows predictable physics principles—especially when air resistance is ignored. Understanding the maximum height reached by such a projectile is essential in fields like ballistics, engineering, and sports science. In this article, we’ll analyze a projectile launched at 50 m/s at a 30° angle, calculate its maximum height, and explain the underlying formulas and physics involved.", "---", "## Understanding Projectile Motion Basics", "A projectile launched from the ground follows a parabolic trajectory under gravity. Ignoring air resistance, the only acceleration acting on the projectile is downward due to gravity: approximately 9.8 m/s². The initial velocity splits into horizontal and vertical components, with the vertical component mainly responsible for the height.", "---", "## Step 1: Break the Initial Velocity into Vertical and Horizontal Components", "The initial speed is 50 m/s at an angle θ = 30° above the horizontal.", "- Vertical component of velocity:\n [\n v_{y} = v \cdot \sin(\ heta)\n ]\n [\n v_{y} = 50 \cdot \sin(30^\circ) = 50 \cdot 0.5 = 25 \ ext{ m/s}\n ]", "---", "## Step 2: Use Kinematics to Find Maximum Height", "At maximum height, the vertical component of velocity becomes zero (the projectile stops rising). We apply the kinematic equation:\n[\nv_y^2 = v_{y,0}^2 - 2g h\n]", "Where:\n- ( v_y = 0 ) m/s at peak\n- ( g = 9.8 ) m/s²\n- ( h ) is the maximum height\n- ( v_{y,0} = 25 ) m/s", "Rearranging the formula to solve for ( h ):\n[\n0 = (25)^2 - 2 \cdot 9.8 \cdot h\n]\n[\n625 = 19.6 \cdot h\n]\n[\nh = \frac{625}{19.6} \approx 31.89 \ ext{ meters}\n]", "---", "## Conclusion", "When a projectile is launched upward from the ground at 50 m/s at a 30° angle, the maximum height achieved is approximately 31.89 meters, assuming no air resistance. This value results from balancing vertical motion under gravity, demonstrating the powerful predictive capability of classical physics in projectile motion problems.", "For practical applications—such as designing ballistic trajectories or optimizing sports techniques—understanding this maximum height ensures accurate and safe launch parameters, enhancing both performance and safety.", "---", "### Keywords for SEO:\nprojectile motion, maximum height calculation, kinematics, vertical velocity, physics projectile, launch trajectory, 50 m/s launch angle 30 degrees, gravity acceleration, projectile launch height."]
