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On Earth, the height, h, in metres, of a free-falling object after t seconds can be modelled by the function h(t) = -4

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On Earth, the height, h, in metres, of a free-falling object after t seconds can be modelled by the function h(t) = -4.9t² + k, while on Venus, the height can be modelled by h(t) = -4.45 t² + k, where t ≥ 0 and k is the height, in metres, from which the object is dropped. Suppose a rock is dropped from a height of 60 m on each planet. For each planet,

(a) Determine the average rate of change of the height of the rock after the first 3 seconds after it is dropped.

(b) Estimate the instantaneous rate of change of the rock 3 seconds after it is dropped on Venus. (Use centred interval method)

(c) Estimate the instantaneous rate of change of the rock on Earth at 2 seconds. (Use centred interval method)

(d) Compare your answer for (b) and (c). What do they represent?