Ask a New Question
Menu

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. (3 points) The initial jump would be represented by a quadratic function. The swim across the pool would be represented by a constant function because there is no height change. Climbing the ladder would be represented by a linear function due to the constant rate and height change.

1 answer

In this situation, we can effectively represent your height relative to time using different types of functions for each distinct phase of your activity:

  1. Jumping into the Water:

    • Quadratic Function: The initial jump can be modeled by a quadratic function because your height changes in a parabolic manner as you ascend and then descend towards the pool. The upward portion of the trajectory can be described by a quadratic function, which captures the effect of gravity on your jump. This function would start at a height of zero (at the ledge), increase to a maximum height at the peak of your jump, and then decrease back to the height of the water surface.

  2. Swimming Across the Pool:

    • Constant Function: Once you hit the water, your height remains constant while you swim. This can be represented by a horizontal line (constant function) on a graph, where your height stays at the same level as the surface of the water for the duration of the swim. This portion of the function does not change with time, indicating no vertical movement.

  3. Climbing Up the Ladder:

    • Linear Function: After you finish swimming and start climbing up the ladder, your height begins to increase again, which can be represented by a linear function. In this case, the height increases at a constant rate, resulting in a straight line that slopes upward. The slope of this line would represent your climbing rate, which remains consistent until you reach the top of the ladder.

Summary of Function Types:

  • Jump: Quadratic Function (parabolic trajectory)
  • Swimming: Constant Function (horizontal line)
  • Climbing: Linear Function (straight line with a positive slope)

In graphing these components, you would see a rise (jump), a flat line (swim), and then another rise (climb), clearly distinguishing the different phases of the activity through the types of functions applied.