Problem1 If we assume negligible air friction and ignore the curvature of the Ea

Question

Problem1 If we assume negligible air friction and ignore the curvature of the Earth, a ball that is thrown into the air from any point on the Earth's surface will follow a parabolic flight pattern (see Figure A). The height of the ball at any time i after it is thrown is given by Where yo is the initial height of the ball above the ground, vyo is the initial vertical velocity of the ball and g is the acceleration due to the Earth's gravity. The horizontal distance (range) traveled by the ball as a function of time after it is thrown is given by: x(t)xo+ xot Where xo is the initial horizontal position of the ball on the ground, Vio is the initial horizontal velocity of the ball. Origin (Figure A) Impact x (Figure 8) If the ball is thrown with some initial velocity vo at an angle ? degrees with respect to the Earth's surface, then the initial horizontal and vertical components of velocity will be: xoDocose Assume that the ball is initially thrown from a position (xo, yo) (0, 0) with an initial velocity vo of 20 meters per second at an initial angle of 0 degrees. Write a program that will plot the trajectory of the ball and determine the horizontal distance traveled before it touches the ground again. The program should plot the trajectories of the ball for all angles 0 from 5° to 85° in 10° steps, and should determine horizontal distance travelled for all angles ? from 0° to 90° in 1° steps. Finally, it should determine the angle that maximizes the range of the ball, and plot the trajectory in a different color.

Explanation / Answer

figure;
Axes = axes('NextPlot', 'add');
time = 100;
%Plotting of trajectories
for angle=5:10:85
[x,y] = trajectoryPlot(angle, time);
plot(x, y,'Parent', Axes);
hold on;
end

%Determining horizontal distance
%Initial velocity
v=20;
for angle=0:1:90
horizontal_dist=v*cosd(angle)*time
end

function [x,y]=trajectoryPlot(ang,time)
%Initial point
x0=0;
y0=0;
%Angle calculation
angle=ang*(pi./180);
%Initial velocity
v=20;
%Gravity
g=9.81;
t=0:0.1:time;
x=x0+v*cos(angle)*t;
y=y0+v*sin(angle)*t-(g*t.^2)/2;
end

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