A drone ascends vertically from ground level at time seconds
MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
A drone ascends vertically from ground level at time t=0 seconds. Its altitude (in meters) for 0≤t≤10 seconds is modeled by the continuous function
s(t)={0.8t2,20+3(t−5),0≤t<5,5≤t≤10.
However, due to a brief sensor malfunction at t=5 seconds, the recorded value s(5) was mistakenly stored as 19 meters instead of the true value predicted by the model.
(1) Part 1: (a) Determine the correct altitude of the drone at t=5 seconds according to the model and decide whether the recorded value introduces a discontinuity at that instant.
(2) Part 2: (b) Considering the recorded data set that includes the erroneous value s(5)=19, assess whether the Intermediate Value Theorem guarantees the existence of a time t in [4,6] at which the drone’s altitude was exactly 21 meters. Clearly reference the theorem’s hypotheses in your reasoning.
(3) Part 3: (c) Suppose the recorded data are corrected so that s(5) matches the model. Explain how this correction alters the conclusion in part (b), again citing the relevant hypotheses.