Question

I want the math lab code for theses problems in a unique way

Theory A projectile is launched from point A up an incline plane that makes an angle of 10 with the horizontal. The mountain is 6,000 m high. Vo 10° Figure 1: Flightpath of a projectile. If we neglect the air resistance, the flight path of a projectile launched at an initial speed vo and an angle θ of departure relative to the horizontal is a parabola (see Fig. 1 ). If we assume that the projectile is launched from the sea level, i.e, at yo 0, then the altitude of the projectile as a function of time is where g-9.81 ms2 is the gravitat nal constant, r is time (in seconds), and V so sin θ (in meters per second). The horizontaf distance of the projectile from the launching position as a function of time is x(t) = Ut , where U= vo cos θ The velocity of the projectile in the horizontal direction, ie, parallel to the x-axis, IS u(t)-U and the velocity in the vertical direction, i.e., parallel to the y-axis, is v(c)gt + V If we include the effects of air resistance, then the altitude of the projectile as a function of time can be approximated as y(t) =-E + ( 1-e-kt), where k is the coefficient of resistance (with the unit 1/s). The horizontal distance of the projectile relative to the initial position as a function of time is x(t) =知-e-kt) The velocity of the projectile in the horizontal direction is and in the vertical direction Deliverables 1. A MATLAB function, flightpath.m, capable of calculating the flight path of a projectile, with and without air resistance, given an initial speed vs. an angle θ of departure relative to the horizontal, and a coefficient of resistance k Use Eqns. (1)-(8). 2. A script, main_flightpaths.m, which uses the function flightpath.m to calculate and the function plot _flightpaths.m to plot the following: a. Altitude, y, as a function of horizontal distance, x (see Fig 2) b. Altitude, y, as a function of time, r c. Horizontal velocity, u, as a function of time, r d. Vertical velocity, v, as a function of time, r For these plots, assume v,-600 ms, θ-60 deg. and k [0 0.005 0.01 0.02 0.040.08]s Figure 2: Altitude versus distance. 3. A script, main_ range.m, which uses the function flightpath.m to calculate and function plot range.m to plot the following a. Range as a function of k b. Total flight time as a function of k For these plots, assume vt p 600 ms, θ with step size of 0.001 s 60 deg, and k from 0 to 0.08 s. 4. A detailed report describing the problem, your solution approach, and your results. Be sure to discuss and comment on your results. Show your MATLAB codes and the output from the code when you execute it. Remember to include appropriate comments in the MATLAB code. The following table summarizes the codes you need to write: m-file Description flightpath.m function that calculates the characteristics of the projectile Input: vo, 8,k Output: Range, flight time, speed/position as a function of time (vectors: t, u, v, x, y) main_flightpathsm A script which initializes parameters and calls flightpath.m and plot flightpaths.m plot_flightpaths.m A function which plots several plots (see part 2) main_range.m A script which initializes parameters and calls flightpath.m and plot_range.m plot rarge m A function which plots several plots (see part 3) Note: if you are using any MATLAB built-in functions to solve nonlinear equations in your project, then in your report you mast explain in detail how these functions work and the method/theory behind them

Answer 1

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