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projectile question (calculate return time and compare them)

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Zeynep Toprak
Zeynep Toprak 2020-3-1
评论： darova 2020-3-1
I Have a question from a textbook
where some equations are written wrong. The correct versions of them are as follows:
v(t)=(-mg/k)+(v0+(mg/k))*(1-exp(-kt/m))
y(t)=-(m-g-t/k)+(m/k)(v0+(mg/k))(1-exp(-kt/m))
for part-c
v_bar = - gt +v0
y_bar = - ((gt^2)/2) + v0t
I do the first and second parts (a, b) as follows. But I am not definitely sure about my results.
In addition to this, I could not create any code for part-c. Please I'm asking for a help to do such type question.
function projectile = max_height( m, k )
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
g = 9.8;
v0 = 25;
t = 0:0.1:12;
v = - (m*g/k) + ((v0 + (m * g/k)) * exp(- k * t /m));
y = - (m*g*t/k) +((m/k)*(v0 +(m*g/k))*(1-exp(- k * t /m)));
plot(t,y);
[max_height, t] = max(y)
end
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Zeynep Toprak
Zeynep Toprak 2020-3-1
v(t)=0. Then I will find the root of v(t)=0 for t. That's, I will draw t from v(t)=0. Right?
darova
darova 2020-3-1
I believe that you should find it numerically. But velocity will never be 0
MATLAB doesn't know where is the ground
You can use find to find first negative value
plot(t,y);
ix = find(y < 0,1);
hold on
plot(t(ix),y(ix),'or')
hold off

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