Question

Using MATLAB

The range of an object shot at an angle θ (with respect to x-axis), with the initial velocity of V0 (in the absence of air resistance), is calculated by the following formula: range=(Vo^2/g)(sin(2theta)) where (0<=theta<=pi/2) And the trajectory of object is given by:     h=tan(theta).x-(g/2Vo^2*cos^2(theta)).x^2 .Where h is the height of the object at each x location and g = 9.81 m/s2.

a) Using π/8 increment size for the angle and V0 = 10 m/s, plot the trajectories of the object in one figure with respect to x.

Hint: follow these steps:

1) For each value of θ find the range.

2) Create x as a vector starting from 0 to the computed range.

3) Compute h using θ and x from steps 1 and 2.

4) Plot h as a function of x.

5) Use hold on for the next plot (Use different colors for the plots and don’t forget to put legends and labels).

b)Create a vector for θ including 100 equally-spaced elements, and determine at which angles the maximum and minimum ranges occurs.

c)What is the max. height of the object at the angle determined in part b.

Answer 1

%get the initial velocity

v0=input(‘Enter the initial velocity’)

Theta=0:pi/100:pi/2;

g=9.81;

% calculate the range

Range=(v^2/g)*(sin(2*theta));

maxRange=0;

in=0;

% find the maximum range

for i=1:length(Range)

             if Range>max Range

                             maxRange=Range;

                             in=I;

                 end

end

% find the maximu angle