Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Matrices
  • Complex Numbers
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • Transformations & asymptotes
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Trig equations & identities
  • Vectors
  • Graph Theory
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
  • Differential Equations
Other
  • Review Videos
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex

    Modelling (Lesson 8/10)

    Non-linear piecewise models

    1 / 3

    Discussion

    John throws a tennis ball up into the air, watches it fall, and lets it bounce until it finally comes to rest on the ground. The bouncing ball and its height versus time are shown below.

    Powered by Desmos

    Combine modelling skills that you have already learned to describe the height of the ball as a function of time.

    Solution:

    We observe that the complete height–time graph consists of four “flight” arcs, each one a downward‐opening parabola whose peak is lower than the one before.


    Putting it all together, h(t) is a piecewise function made up of these four downward‐opening parabolas, each defined on one of the successive time‐intervals and each with a smaller top height than the previous one.


    Thus, the motion of the ball combines what we learned about quadratic models and linear piecewise models!