Discover

Air resistance causes objects falling to Earth to fall at different rates. If air resistance is removed, all objects drop at the same rate. The video “The Hammer and Feather” shows two objects falling in a vacuum (i.e., there is no air resistance).

Image Credit: Apollo 15 Crew, NASA

Try This 1

For objects falling near the surface of Earth, the function d = 5t2 approximately models the time, t, in seconds, for an object to fall a distance, d, in metres, if the resistance caused by air can be ignored.

1.  
   1. Identify any restrictions on the domain of the function d = 5t2. Why are these restrictions necessary?
   2. What is the range of the function?
   3. Create and complete a table similar to the following for the function d = 5t2.

       

      t	d

   4. Create a graph showing the distance fallen as a function of time.
2. 
   
   1. Determine the equation of the inverse function of d = 5t2.
   2. Create and complete a table of values similar to the following, and then graph the inverse function.1

       

      t	d

Save your responses in your course folder.

Share 1

With a partner or in a group, compare and describe the original function and the inverse function in terms of domain, range, and shape of graph.

If required, save a record of your discussion in your course folder.

1 Adapted from Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.