Welcome to our study of horizontally launched projectiles. A horizontally launched projectile is an object that is launched with an initial velocity that is purely horizontal from a certain height above the ground. The key characteristics include zero initial vertical velocity, constant horizontal velocity, gravity acting only vertically downward, and motion following a parabolic path.
Now let's analyze the motion components separately. The horizontal motion has no forces acting on it, so the horizontal velocity remains constant throughout the flight. The position in the x direction is simply the initial horizontal velocity times time. The vertical motion is different - gravity acts downward with acceleration g equals 9.8 meters per second squared. Since the initial vertical velocity is zero, the vertical position follows the equation y equals h minus one half g t squared, and the vertical velocity becomes negative g t.
Let's examine the key equations for horizontally launched projectiles. For horizontal motion, the position is simply the initial horizontal velocity times time. For vertical motion, the position equation is y equals h minus one half g t squared, and the vertical velocity is negative g t. Two important derived formulas are the time of flight, which equals the square root of two h over g, and the horizontal range, which is the initial horizontal velocity times the time of flight.
Let's solve a practical example. A ball is launched horizontally from a cliff 20 meters high with initial velocity 15 meters per second. First, we find the time of flight using t equals square root of 2h over g, which gives us 2.02 seconds. The horizontal range is the initial velocity times time, giving us 30.3 meters. For the final velocity, the horizontal component remains 15 meters per second, while the vertical component is negative g times t, giving us negative 19.8 meters per second. The magnitude of the final velocity is 24.8 meters per second.
To summarize what we've learned about horizontally launched projectiles: They start with zero initial vertical velocity and follow independent horizontal and vertical motion components. The horizontal velocity remains constant while vertical motion follows free fall under gravity, creating a characteristic parabolic trajectory path.