The altitude (in meters) of a sounding rocket at time (in seconds) after launch is…

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

The altitude

H

(in meters) of a sounding rocket at time

t

(in seconds) after launch is recorded in the table below.

$t$ (s)	6.4	6.8	7.0	7.2	7.6
$H(t)$ (m)	524	556	568	578	596

Answer the following questions about the rocket’s vertical velocity. (a) Using the data in the table, estimate the instantaneous vertical velocity of the rocket at

t=7.0\text{ s}

. Show all computations. (b) Estimate the velocity again using only the data at

t=7.0\text{ s}

and

t=7.6\text{ s}

. Compare this result with your estimate from part (a), and discuss which estimate you expect to be more accurate and why. (c) Suppose the altitude measurement at

t=7.2\text{ s}

is subject to an error of

\pm3\text{ m}

. Determine the resulting range of possible values for the estimate you obtained in part (a). Explain your reasoning.

Related theory

Error Analysis
Derivative Foundations

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