Question

-8(0) dt 25.22 Suppose that a projectile is launched upward from the earth's surface. Assume that the only force acting on the object is the downward force of gravity. Under these conditions, a force balance can be used to derive, dυ R? (R + x)2 where v = upward velocity (m/s), t = time (s), x = altitude (m) measured upwards from the earth's surface, g(0) = the gravita- tional acceleration at the earth's surface (= 9.81 m/s?), and R = the earth’s radius (= 6.37 x 10° m). Recognizing that dx/dt = v, use Euler's method to determine the maximum height that would be obtained if u(t = 0) = 1500 m/s.

solve it with matlab

Answer 1

`Hey,

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format long

R=6.37e6;

g=9.81;

f=@(t,y) [y(2);-(R^2*g)/(R + y(1))^2];

[T,Y]=eulerSystem(f,[0,1000],[0,1500],0.1);

disp('Maximum height is');

max(Y(1,:))

function [t,y]=eulerSystem(Func,Tspan,Y0,h)

t0=Tspan(1);

tf=Tspan(2);

N=(tf-t0)/h;

y=zeros(length(Y0),N+1);

y(:,1)=Y0;

t=t0:h:tf;

for i=1:N

y(:,i+1)=y(:,i)+h*Func(t(i),y(:,i));

end

end

Of 1971 6 7 8 - 9 10 11 12 - 13 14 15 - 16 - 17 - 18 19 20 21 - 22 g=9.81; f=@(t,y) [y(2);-(R^2*g)/(R + y(1))^2); [T,Y]=eulerSystem(f, [0,1000], [0,1500],0.1); disp('Maximum height is'); max(Y(1,:)) function [t,y)=eulerSystem(Func, Tspan, Yo, h) tø=Tspan(1); tf=Tspan(2); N=(tf-to/h; y=zeros(length(Y0),N+1); y(:,1)=YO; t=t0:h:tf; for i=1:N y(:,i+1)=y(:,1)+h*Func(t(i),y(:,1)); end end X Command Window New to MATLAB? See resources for Getting Started. Maximum height is ans = 1.168553880993685e+05 fx >> ction.m

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