Geometric Locus of Thrown Point Masses at Time t1 | Georgia Southern University - Edubirdie

University:
Georgia Southern University
Course:
ENGR 2232 | Dynamics of Rigid Bodies
Academic year:

2024
Views:

398

Pages:

1
Author:

Jalen W.

Problem 2.7: Determine the geometric locus of all points P1, which are the positions of point masses thrown at time t=0 with the same initial velocity v0 from a point P under different angles α with respect to the horizontal. The trajectories are assumed to be in the same vertical plane without air drag. The goal is to find the path followed by these point masses at a specific time t=t1. MATLAB Code: % Given initial conditions v0 = 10; % initial velocity g = 9.81; % acceleration due to gravity alpha = 30; % angle with respect to the horizontal t1 = 5; % specific time t=t1 % Calculating the position at time t=t1 for different angles alpha_rad = deg2rad(alpha); x1 = (v0 * t1) * cos(alpha_rad); z1 = -(0.5 * g * t1^2) + (v0 * t1 * sin(alpha_rad)); % Finding the geometric locus of all points P1 radius = v0 * t1; center_z = -0.5 * g * t1^2; disp(['The points P1 are located on a circle with radius r = ', num2str(radius), ' and the center C at z = ', num2str(center_z)]);

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