Final answer:
The function represents the projectile motion of an object, describing its vertical height over time without considering air resistance. The height is initially 1700 feet and decreases as the object falls under the influence of gravity. By setting the height function's derivative to zero, one can find the time at which the maximum height is achieved.
Step-by-step explanation:
The given function h = -16t2 + 1700 describes the height h, in feet, of an object over time t, in seconds. This is a typical example of a projectile motion equation in physics, which is a part of kinematics, the study of motion without considering its causes. The equation includes an initial height of 1700 feet and accounts for the acceleration due to gravity as -32 feet per second squared, adjusted to -16 to match the units of height in feet.
The given function does not consider air resistance or any other forces that might affect the projectile's motion. Normally, if air resistance were considered, the object would reach a lower elevation due to the decelerating force of the drag. The quadratic nature of the function indicates that the height of the object will increase to a certain point and then decrease as the object falls back towards the ground.
For projectiles, the maximum height is reached when the vertical velocity component becomes zero, which can be determined using calculus or by setting the derivative of the height function to zero and solving for time t.