Question

In 1-2 sentences, describe what types of function can be used to describe each part of the following situation. You jumped from a high ledge into a pool of water, then swam to the other side of the pool and climbed up a ladder at a constant rate to get out of the pool. Compare your height around the surface of the pool water to the time.

Answer 1

While falling from the ledge your height vs. time is quadratic (a parabola) because of constant gravitational acceleration; while swimming at the surface your height is essentially constant (a horizontal line); and climbing the ladder at a steady pace is linear (a straight line). The whole motion is best described as a piecewise function that joins these three parts.