Use the falling object model, h=-16 t^2+s . Given the...

Use the falling object model, $h=-16 t^{2}+s .$ Given the initial height $s$, find the time it would take for the object to reach the ground, disregarding air resistance. Round the result to the nearest tenth.
$s=48$ feet

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Key Concepts

Kinematics of Free-Fall

This concept involves the study of motion, particularly of objects moving under the influence of gravity. The falling object model h = -16t² + s reflects the distance fallen over time with the constant gravitational acceleration (in feet per second squared) acting on the object.

Quadratic Equations in Motion

When solving for the time it takes an object to reach the ground, setting the height h to zero results in a quadratic equation in terms of time t. Solving this equation typically requires using algebraic techniques such as factoring or the quadratic formula.

Assumptions in Physics Models

The provided model assumes that air resistance is negligible, meaning that the only force acting on the falling object is gravity. This simplification allows for the use of a constant acceleration term, leading to more straightforward calculations.

Rounding in Mathematical Calculations

Rounding is a process used to simplify numerical results to a desired degree of precision. In this context, after solving the quadratic equation for time, the value is rounded to the nearest tenth to provide an easily interpretable answer.

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