uestion6 altitude in meters during the 48 hours following the launch of a weathe

Question

uestion6 altitude in meters during the 48 hours following the launch of a weather balloon: h(t)-0.12t12t 30ot+4100t 220 Assume that the unit of t is hours al Use MATLAB together with the fact that the velocity is the first derivative of the altitude to dete the equation for the velocity of the balloon. b/ Use MATLAB together with the fact that acceleration is the derivative of velocity, or the second c/ Use MATLAB tive of the altitude, to determine the equation for the acceleration of the balloon. to determine when the balloon hits the ground. Because hit) is a-fourth order there will be four answers. However, only one answer will be physically meaningful polynomial, d/ Use MATLAB's symbolic plotti ng capability to create plots of altitude, velocity, and acceleration from time 0 until the balloon hits the ground [which was determined in part (c)l. You'll need three separate plots, since altitude, velocity, and acceleration have different units e/ Determine the maximum height reached by the balloon. Use the fact that the velocity of the balloon is zero at the maximum height

Explanation / Answer

The matlab script used to do the above tasks is given below:

Matlab script:

clear variables
close all

%%
% Define symbols and expressions
syms t;
h = -0.12*t^4+12*t^3-300*t^2+4100*t+220;

% Calculate expressions for velocity and acceleration
v = diff(h,t);
a = diff(v,t);

% Solve for time when balloon hits ground
tSolution = solve(h,t);
tFinal = tSolution(real(tSolution)>0&imag(tSolution)==0);
tFinal = double(tFinal);

% Plot height, velocity and acceleration as a function of time
ezplot(h,[0 tFinal]); xlabel('Time (hours)');ylabel('Height (m)');
figure;
ezplot(v,[0 tFinal]); xlabel('Time (hours)');ylabel('Velocity (m/hr)');
figure;
ezplot(a,[0 tFinal]); xlabel('Time (hours)');ylabel('Acceleration (m/hr^2)');

% Calculate time at which the balloon is at maximum height.
tSolutionv = solve(v,t);
tSolutionv = double(tSolutionv);
tMaxHeight = tSolution(real(tSolutionv)>0&imag(tSolutionv)==0);
tMaxHeight = double(tMaxHeight);
% End of matlab script

e):

The balloon is at its maximum height when the velocity is zero.

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