Question

A new type of bird capable of self-propulsion is designed in order to maximise its flying distance in the presence of aerodynamic drag. This new bird, having the initial mass of mo, generates thrust by ejecting 1% of its initial mass (0.01mo) with the velocity of 50m/s in the direction opposite to the bird’s instantaneous velocity relative to the bird every 0.1s (similar to how rockets generate thrust).

function [vx_f,vy_f,m_f] = mass_ejection(vx_i,vy_i,v_eb,m_i,m_e)

% Inputs:

% vx_i: Velocity component in x direction before ejection

% vy_i: Velocity component in y direction before ejection

% v_eb: Ejection velocity of the mass relative to the bird

% m_i : Mass of the bird before ejection

% m_e : Ejection mass

% Outputs: % vx_f: Velocity component in x direction after ejection

% vy_f: Velocity component in y direction after ejection

% m_f : Mass of the bird after ejection

(d) Using the function written incorporate the mass ejection mechanism into the existing model with drag (remember that you need to run this function every 0.1s and use the output to update the velocity and mass of the bird). Compute and plot the trajectory of the new bird and compare it with the trajectory of the original bird with the same initial conditions. On your plot, indicate with symbols where mass ejections happen. The bird is launched with the initial velocity of 10m/s at the angle of 50? from the horizontal. The initial mass of the bird, mo is 1kg. The release point of the bird is 2m directly above the base of slingshot and the base of slingshot can be considered as the origin (figure 5). The density of air is 1.2 kg/m3 and use CD = 1. The bird can be treated as a sphere with a radius of 0.15 m. on matlab

Answer 1