Final answer:
The question pertains to the physics of projectile motion, specifically the height of a stone thrown upward as a function of time given the initial velocity and acceleration due to gravity.
Step-by-step explanation:
The question is about a stone thrown upward with an initial velocity, and the equation that describes its height over time h(t) = -16t² + 144t. To solve for the height at any given time t seconds, this equation incorporates the acceleration due to gravity (-16 ft/s²) and the initial velocity (144 ft/s). For a comprehensive discussion, one would need to calculate the maximum height of the stone, the time it takes to reach that height, and when the stone hits the ground (assuming it is launched from the ground level).
Parts of such a question may include finding the time it takes to reach the maximum height, which is done by setting the derivative of h(t) to zero and solving for t. To find the total time in the air, one would need to solve for when h(t) equals zero. Additionally, the velocity of the stone at any time t can be found by taking the derivative of h(t), resulting in the velocity function v(t) = -32t + 144.