Question

In a 7th graders response show your work
In 1. 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. (2 points)

Answer 1

- Jumping off the ledge: your height vs. time is modeled by a quadratic (a parabola) because gravity makes you speed up as you fall, so height changes faster and faster — e.g. y = h0 + v0t − 4.9t^2 (meters).
- Swimming across at a steady depth: your height is a constant function (a horizontal line) because your vertical position does not change while you swim.
- Climbing the ladder at a constant rate: your height is a linear function (a straight line) because you go up the same amount every second, y = mt + b.

All together the height-vs-time graph is a piecewise function made of a parabola (fall), a constant segment (swim underwater), and a straight line (climb); heights above the water surface are positive, at the surface are zero, and underwater are negative.