Question

Kay drops a ball from 5 feet. The height of Kay’s ball can be represented by -16t^2 + 5 after t seconds. At the same time, Sam throws a ball upward. The height of Sam’s ball can be represented by -16t^2 + 24t + 3 after t seconds. The difference in heights represented by the polynomials is an example of the:

A. Position-Time Function
B. Height-Time Function
C. Quadratic Function
D. Kinematic Equation

Answer 1

The difference in heights of the balls after time t can be classified as a Height-Time Function, which is a type of quadratic function representing the vertical motion of the balls.

Step-by-step explanation:

The difference in heights of Kay's and Sam's balls after t seconds can be best classified as a Height-Time Function. The polynomial expressions given for each ball's height with respect to time (t) are examples of quadratic functions, which describe the motion of the balls under gravity, assuming no air resistance. To find the difference in heights, you simply subtract one polynomial from the other.

To illustrate, at t seconds, Kay's ball is at a height of -16t2 + 5, and Sam's ball is at -16t2 + 24t + 3. Subtracting the first polynomial from the second gives us (-16t2 + 5) - (-16t2 + 24t + 3), which simplifies to 24t - 2. The resultant polynomial still describes a Height-Time relationship and reflects the difference in height between the two balls as a function of time.