an experiment to estimate acceleration due to gravity. He dropped several He col

Question

an experiment to estimate acceleration due to gravity. He dropped several He collected his data in the following chart. Using the data in the chart and a graphing utility, the tops of buildings of different heights and recorded the time it took for the watermelons to watermelons from hit the ground. find the power function s(t) of best fit. Round all answers to four decimal places. Time (seconds) Building Height (ft) 10 11160 20 14760 16780 19380 35 45 60 s(t)-16.02331.9982 C)stt) 24.066581.8707 n(t) = 17.9792t21 834 D) s(0)-15.9727 2.0018

Explanation / Answer

matlab code

close all
clear
clc

% s = a*t^b;
% log(s) = log(a) + b*log(t);
% s_ = a_ + b*t_;
t_ = log([0.7907 1.116 1.476 1.678 1.938]);
s_ = log([10 20 35 45 60]);

% alpha = [b; a_];
A = ones(length(t_), 2);
A(:,1) = t_';
alpha = pinv(A)*s_';
b = alpha(1);
a = exp(alpha(2));
fprintf('s(t) = (%.4f)*t^(%.4f) ',a,b);

output

s(t) = (16.0233)*t^(1.9982)

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