# Velocity of a Weather Balloon

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Ertugrul Icer on 16 Jun 2020
Commented: Image Analyst on 17 Jun 2020
Let the following polynomial represent the velocity of a weather balloon following the launch:
v(t) = -0.25*t.^3 + 36*t.^2 - 760t + 4100
Here, "t" needs to be dened as a symbolic variable. By using the given velocity polynomial, construct a MATLAB code to:
a) Find the altitude polynomial of the balloon in terms of t where constant term of the altitude polynomial is dened as "9".
b) Determine when the balloon hits the ground (Your code should give one exact answer as an acceptable numerical value for t).
c) Obtain plots of altitude and velocity from time 0 until the balloon hits the ground by using the command "ezplot".

David Hill on 16 Jun 2020
What have you done? Do you have a specific question?
Ertugrul Icer on 16 Jun 2020
I couldn't write the code the question asked for

David Hill on 16 Jun 2020
I will give you a start:
syms t;
v=-0.25*t.^3 + 36*t.^2 - 760*t + 4100;
s=int(v)+9;
a=diff(v);
ezplot(s,[0,155.7]);
figure;
ezplot(v,[0,155.7]);

David Hill on 16 Jun 2020
Your instructions say to use a symbolic variable. Much easier without symbolic.
v=[-.25,36,-760,4100];
s=polyint(v,9);
a=polyder(v);
t=0:.1:155.7;
plot(t,polyval(v,t));
figure;
plot(t,polyval(s,t));
Ertugrul Icer on 16 Jun 2020
i think its true but why; why u write like (v=[-.25,36,-760,4100];) how can be possible without using (t)
David Hill on 17 Jun 2020
Because it is a polynomial and matlab has special functions that support polynomials.

Image Analyst on 17 Jun 2020
Another hint:
t = linspace(0, 125, 1000);
v = -0.25*t.^3 + 36*t.^2 - 760*t + 4100 % Your equation
% Now plot it:
plot(t, v, 'b-', 'LineWidth', 2);
grid on;
xlabel('t', 'FontSize', 20);
ylabel('Velocity', 'FontSize', 20);
% Draw a line at v=0
yline(0, 'Color', 'black', 'LineWidth', 2);

#### 1 Comment

Image Analyst on 17 Jun 2020
Another hint: roots() function.