Example 1
Completion requirements
| Example 1 |
Marie-Claire and Leo went skydiving from an altitude of \(2 \thinspace 000 \thinspace \rm{m}\). Leo jumped first and opened his parachute immediately after leaving the plane. Five seconds later, Marie-Claire jumped and allowed herself to free-fall before opening her parachute.
The first part of each diver’s descent can be modelled by the following equations, where \(h\) represents the height, \(t\) seconds after Leo jumps.
Leo: \(h = 2 \thinspace 000 - 4t , t \ge 0\)
Marie-Claire: \(h =-4.9t^2 + 49t +1 \thinspace 877.5, t \ge 5\)
The first part of each diver’s descent can be modelled by the following equations, where \(h\) represents the height, \(t\) seconds after Leo jumps.
Leo: \(h = 2 \thinspace 000 - 4t , t \ge 0\)
Marie-Claire: \(h =-4.9t^2 + 49t +1 \thinspace 877.5, t \ge 5\)
-
Sketch a graph of the system.
-
Determine the point of intersection of the two graphs.
The two graphs intersect at approximately \((7.47, 1 \thinspace 970.12)\).
-
Explain what the point of intersection of the two graphs represents.
Approximately \(7.5\) s after Leo leaves the plane, Marie-Claire will pass him at an altitude of approximately \(1 \thinspace 970\) m.
