function:

function y = hitTheSpot(v0,theta) Cd = 0.5; dxdt = @(t,x) [x(3:4);(-1/2*1*pi*(0.1^2)*Cd*norm(x(3:4))*x(3:4)-[0;9.81])]; if size(v0) == size(theta) [m,n] = size(v0); y = zeros(m,n); for i = 1:m for j = 1:n [t,x] = ode45(dxdt,[0,2*v0(i,j)*sind(theta(i,j))/9.81],[0;0;v0(i,j)*cosd(theta(i,j));v0(i,j)*sind(theta(i,j))]); % figure % plot(x(:,1),x(:,2)) % hold on % plot(v0*cosd(theta)*t,v0*sind(theta)*t-1/2*9.81*t.^2) % set(gca,'ylim',[0,inf]) [~,b] = max(x(:,2)); y(i,j) = interp1(x(b:end,2),x(b:end,1),0,'pchip'); end end elseif size(v0) == [1,1] [m,n] = size(theta); y = zeros(m,n); for i = 1:m for j = 1:n [t,x] = ode45(dxdt,[0,2*v0*sind(theta(i,j))/9.81],[0;0;v0*cosd(theta(i,j));v0*sind(theta(i,j))]); % figure % plot(x(:,1),x(:,2)) % hold on % plot(v0*cosd(theta)*t,v0*sind(theta)*t-1/2*9.81*t.^2) % set(gca,'ylim',[0,inf]) [~,b] = max(x(:,2)); y(i,j) = interp1(x(b:end,2),x(b:end,1),0,'pchip'); end end elseif size(theta) == [1,1] [m,n] = size(v0); y = zeros(m,n); for i = 1:m for j = 1:n [t,x] = ode45(dxdt,[0,2*v0(i,j)*sind(theta)/9.81],[0;0;v0(i,j)*cosd(theta);v0(i,j)*sind(theta)]); % figure % plot(x(:,1),x(:,2)) % hold on % plot(v0*cosd(theta)*t,v0*sind(theta)*t-1/2*9.81*t.^2) % set(gca,'ylim',[0,inf]) [~,b] = max(x(:,2)); y(i,j) = interp1(x(b:end,2),x(b:end,1),0,'pchip'); end end end

Please code in matlab

2) 1D domain interpolation from a function Download hitTheSpot.m from canvas, the function you used as a part of Homework 2. As a reminder, hitThe Spot is a function that, when given an initial speed and angle above the horizontal, predicts how far away a projectile will land. This is called the range. Generate data from hitTheSpot.m for the range using angle values 0 [5*,85), 40 = 10%,vo = 35 m/s then use interpolation to get the following results a) Linear interpolation to find the projectile range for 0 = 30. Save the value on HW4_3.dat b) Spline interpolation to find the projectile range for 0 = 30. Save the value on HW4_4.dat