How to model an equation?

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Danny Maefengea 2020-9-11

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评论： Danny Maefengea 2020-9-11

Hi there, I have been trying to think of how to model the problem bellow in MATLAB but I couldn't. Can anybody help here please?

Thank you very much for your help.

A ball starts falling down through dense liquid. Its velocity (in cm/s) is given by the equation: dv/dt = 1.6 − 0.025v^2 .

If v(0) = 0cm/s, show that it will take approximately 6.77s for the ball to reach a velocity of 7.0cm

If the container is 1 meter deep, determine, the time the ball has reached the bottom.

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Alan Stevens 2020-9-11

Type help ode45 in the Matlab workspace.

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Answer 1

BOB MATHEW SYJI 2020-9-11

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I think this should work. When you give time t1 for which the velocity you want, and the depth of the container as input, the function returns the velocity at time t1 and the time taken to hit the bottom as the output

function [velocity, time]= diff_eqn(t1,depth)
%Inputs given are time and depth of container
%function returns the velocity at time t1 and
%time taken to hit the bottom of container
syms y(t)
ode = diff(y)+0.025*y^2==1.6;
cond=y(0)==0;
ySol(t)=dsolve(ode,cond);
velocity=double(ySol(t1))
time=depth/velocity
end