Question

Using Matlab:

The range of an object shot at an angle with respect to the x-axis and an initial velocity vo is given by Range = (Vo)²* sin(2*θ)/g
for   0<= θ <= π and neglecting air resistance. Use g = 9.81 m/s² and an initial velocity Vo of 100 meters per second.
Use evenly spacing angle of π/40.

a) find the maximum range in meters

b) find the angle at which the maximum range occurs in radians

*Your answer must be based on the increment specified in this problem π/40.

Explain the process and how you obtained the results.

Answer 1

% Matlab script to determine the maximum range (in meters) and the angle at
% which the maximum range occurs(in radians)

% define the variables
g = 9.81; % m/s^2
Vo = 100; % m/s
max_angle = 0; % radians % initialize max_angle to first value i.e 0
max_range = (Vo^2)*sin(2*max_angle)/g; % meters % calculate and set max_range to range at max_angle

% loop from 0 to pi in steps of pi/40
for i=0:pi/40:pi
% compute range at angle = i
range = (Vo^2)*sin(2*i)/g;
% if range > max_range, update max_range and max_angle
if(range > max_range)
max_range = range;
max_angle = i;
end
end

% display the maximum range value and the angle at which it occurs
fprintf('Maximum range: %f meters at angle: %f radians\n',max_range, max_angle);

%end of script

Output: