Time–lapse photography is used to track the height of an object in metres. The following heights were recorded at times 0.2s, 1.2s and 2.1s respectively: 9.203m, 14.344m and 10.591m.
a) Determine an equation to model the height of the object over time, in seconds, documenting a necessary assumption.
b) Hence determine the maximum height reached by the object.
c) If the object was launched from a height of 5m and continued until it hit the ground, determine the valid domain for the function and interpret this in terms of the timing of the photography and the time the object was in the air
d) Determine the new rule for the function, including the domain, so that t=0 corresponds to the time the object was launched.
e) State any limitations of this modelling process.
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