Velocity of a Weather Balloon

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]

What have you done? Do you have a specific question?

[Ertugrul Icer]

I couldn't write the code the question asked for

Answer 1

[David Hill]

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]);

[Ertugrul Icer]

when i try run that code its give me to the "('syms' requires Symbolic Math Toolbox.)". how can i write it without syms function

[Ertugrul Icer]

i try like that but its give to me again some errors on ezplot line

t=0:155.7;
v=-0.25*t.^3 + 36*t.^2 - 760*t + 4100;
s=-1/16*t.^4+12*t.^3-380*t.^2+4100t+9;
a=diff(v);
ezplot(s,[0,155.7]);
figure;
ezplot(v,[0,155.7]);

[David Hill]

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]

i think its true but why; why u write like (v=[-.25,36,-760,4100];) how can be possible without using (t)

[David Hill]

Because it is a polynomial and matlab has special functions that support polynomials.

Answer 2

[Image Analyst]

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);

[Image Analyst]

Another hint: roots() function.