Question

A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 ft/s. Which graph could represent the leaf's highest point in feet as a function of time in seconds after leaving the branch? 1. A graph that starts at 12 feet and decreases linearly to 0 feet. 2. A graph that starts at 12 feet and decreases exponentially to 0 feet. 3. A graph that starts at 12 feet and decreases parabolically to 0 feet. 4. A graph that starts at 12 feet and decreases sinusoidally to 0 feet.

Answer 1

The correct graph that represents the leaf's highest point as a function of time is a graph that starts at 12 feet and decreases parabolically to 0 feet.

Step-by-step explanation:

The graph that could represent the leaf's highest point in feet as a function of time in seconds after leaving the branch is option 3, a graph that starts at 12 feet and decreases parabolically to 0 feet.

This is because as the leaf falls, its height decreases at an accelerating rate due to the force of gravity. The motion of the leaf can be described by a parabolic function, where the highest point represents the vertex of the parabola.

Option 1, a graph that decreases linearly, does not account for the acceleration of the leaf's fall, while option 2, a graph that decreases exponentially, does not accurately represent the motion of a falling object under the influence of gravity.

Option 4, a graph that decreases sinusoidally, is not applicable to the motion of a falling object and does not accurately represent the leaf's descent.

Learn more about graph representation of a falling object's height