Projectile Trajectory Problem

Solution 

1.3

2.3

3.2

4.6

5.4

6.6

7.6

8.3

9.4

10.1

11.PFAmatlab file and jpg pic

12.4

13.1

14.2

15.4

16.3

17.2

18.1

19.1

20.1

21.3

22.PFAmatlab file

soln_11.m 

t=linspace(0,0.1788,100); % at t=0.1788, y becomes zero

x=3*cosd(17)*t;

y=3*sind(17)*t-0.5*9.81*t.*t;

plot(x,y);

grid on;

xlabel(‘x’);

ylabel(‘y’);

title(‘Trajectory of projectile’);

soln_22.m 

% assume initial velocity as 1 m/s, maximum angle doesn’t depend on initial

% velocity

g=9.81;

syms theta;

t=2*sin(theta)/g;

%range is sin(2*theta)/g assuming initial velocity 1 m/s

R=sin(2*theta)/g;

df=diff(R,theta);

for t=linspace(0,pi/2,99)

if abs(eval(subs(df,t)))==0

angle_req=t;

break;

end

end

disp(angle_req*(180/pi)); %convert into degrees