When an object with a parachute is released to fall freely, its height, h, in
metres, after t seconds is modelled by , where g
is the acceleration due to gravity, r is the resistance offered by the
parachute, and k is the height from which the object is dropped. On
Earth, g 9.8 m/s2. The resistance offered by a single bed sheet is
0.6 m/s2, by a car tarp is 2.1 m/s2, and by a regular parachute is 8.9 m/s2.
a) Describe how the graphs will differ for objects dropped from a height
of 100 m using each of the three types of parachutes.
b) Is it possible to drop an object attached to the bed sheet and a similar
object attached to a regular parachute and have them hit the ground
at the same time? Describe how it would be possible and what the
graphs of each might look like.