engr133_lab02_rsawran
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Liberty University *
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133
Subject
English
Date
Apr 3, 2024
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2
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ENGR 133 - LAB 02
Authored by: Rowan Sawran
Exersice #1 Problem Statement
We are asked to preform some calculations for a projectile, given the equations for horizontal (x-direction) and vertical (y-direction) distance traveled as a function of initial velocity (
Vo
), launch angle (
A
) and time (
t
)., We are given values for Vo
and A
, but x-distance, y-distance, and time are unknown. We want to know the maximum height of the projectile and the corresponding time to create a plot of the entire fligt of the projectile. The equations that applies are:
Problem Solution Process (Psuedocode)
•
Initialize Variables
•
Calculate the total time of projectile fight
•
calculate x(t) and y(t) positions during projectile flight
•
Determine the maximum height of the projectile and the corresponding time
•
Create a plot of the entire flight of the projectile
•
Display flight information as formatted text
Problem Solution
Initialize Variables
clear, clc, close all
Vo = 50; % Initial Velocity, m/s
A = 50; % Launch Angle, degrees
g = 9.81; % Acceleration due to gravity, m/s^2
Calculate the total time of projectile flight
t_hit = (2*Vo*sind(A))/g; % Calculating total projectile flight time, seconds
Calculate x(t) and y(t) positions during projectile flight
t = 0:0.01:t_hit; % Time array, seconds
x_dist = (Vo*cosd(A))*t; % Horizontal distance traveled, meters
y_dist = (Vo*sind(A))*t - 0.5*g*t.^2; % Vertical distance traveled, meters
Determine the maximum height of the Projectile and the corresponding time
[y_max, k] = max(y_dist); % Returns maximum vertical distance & index k
1
t_max = t(k); % Returns the kth value in the time array = time of max height
Create a plot of the entire flight of the projectile
plot(x_dist,y_dist), grid on % Create plot with grid
title(
'Projectile flight, Vo =50 m/s, A=50 deg'
) % Add horiontal axis label
xlabel(
'Horizontal Travel(x_dist)[m]'
) % Add horizontal axis label
ylabel(
'Vertical Travel(y_dist)[m]'
) % Add vertical axis label
Display flight information as formatted text
fprintf(
'The maximum altitude of the projectile is: %.2f meters.\n\n'
, y_max)
The maximum altitude of the projectile is: 74.77 meters.
fprintf(
'This occurs at %.2f seconds after launch. \n\n'
, t_max)
This occurs at 3.90 seconds after launch. fprintf(
'The total flight path is shown above. \n\n'
)
The total flight path is shown above. 2
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