The height in feet of a projectile launched vertically from...

The height in feet of a projectile launched vertically from the ground with an initial velocity of 128 feet per second is given by the function $h(t)=-16 r+128 t,$ where $t$ is in seconds. Calculate and interpret the following.
$$
h(0)
$$

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Key Concepts

Projectile Motion

Projectile motion describes the movement of an object that is launched into the air and is influenced only by gravity (assuming air resistance is negligible). The path of the object is modeled by kinematic equations, which account for the initial launch conditions such as position and velocity and the constant acceleration due to gravity.

Initial Condition

An initial condition specifies the state of a physical system at the beginning of an observation, commonly at time t = 0. For projectile motion, determining the initial condition, such as the initial height or starting position of the object, is essential because it sets the baseline from which all subsequent motion is measured.

Function Evaluation

Function evaluation is the process of calculating the output of a mathematical function by substituting a specific input value. In the context of the projectile's height function, substituting t = 0 allows us to determine the initial height at the moment of launch, providing meaningful information about the system's starting conditions.

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