Final answer:
The question involves understanding projectile motion and its vertical and horizontal components in physics, with specific reference to the influence of gravity on the vertical motion, and how time and initial vertical velocity determine the height reached by the projectile.
Step-by-step explanation:
The student's question about the height of a cannonball after t seconds using the equation h = -16t^2 + 222t + 13 is a physics problem related to projectile motion. Here, the term velocity is crucial because it helps determine the vertical motion of the projectile. Additionally, the fact that an object projected upward or horizontally will have a vertical motion that is independent of its horizontal velocity is a key concept in understanding projectile motion.
To analyze the trajectory of the projectile, we can break the motion into two components: horizontal and vertical. The horizontal component is influenced by the initial horizontal velocity, while the vertical component is subject to gravitational acceleration, which on Earth is approximately 9.8 m/s^2 (approximated in the equation by 16t^2 due to the units used). The equation given includes initial vertical velocity and initial height and describes how the height of the cannonball changes over time, considering the influence of gravity.
It's important to note that the amplitude in vertical velocity corresponds with time spent in the air and the maximum height reached. For example, in the kinematic equations referenced, the term h = ½gt² represents the height reached by an object in free fall after time t, whereas h = g(t−1)² represents the height three-fourths of the way through its motion if it drops 2/3h in the last t-1 seconds.