Write a matlab m file that solves the equations below for...

Write a MATLAB .m file that solves the equations below for the missile trajectory from a given set of initial conditions. Use Δt = 0.005 s. The function should have the following header: function [T, X, Y, Z, U, V, W] = missile(X0, Y0, Z0, m0, mf, Thmag0, theta, phi, Tburn) where the inputs are the initial position, initial and landing mass, initial thrust magnitude, launch angles and burn time of the missile. All inputs are scalars while all outputs are vectors. You need to simulate until the missile lands on the terrain. Use the MATLAB built-in function "interp2." Equations: Where the call format for mass is [m] = mass(t, m0, mf, Tburn), Thrust is [Th_x, Th_y, Th_z] = thrust(t, Thmag0, theta, phi, Tburn, u, v, w), and Drag Coefficient is [Cd] = drag_coeff(Vmag).

Transcript

00:01 All right, it took me a while to figure out what was going on here, but i think i've figured it out.

00:10 I'm going to call this the z direction.

00:15 This into the paper is the y direction, and then this is going to be the x direction.

00:23 Now, there's a missile being fired from 5 ,000 meters away.

00:36 And it is fired at a 20 degree angle at 600 meters per second.

00:53 Now, the anti -ballistic missile is being fired from 500 meters away.

01:03 And it's being fired in the yz plane at 60 degrees to the y within the yz plane, with an initial velocity of v sub -zero.

01:25 All right.

01:27 Now, using this, which took me a long time to figure out what it meant, using this, then i thought about is the rocket, the original rocket aiming for the target, aiming for zero, the origin in this case? so i have the equation that i've used before.

01:50 The range is v initial squared, sine squared theta.

02:00 No, no, no, not sine square of theta, sign of two theta.

02:08 Over g.

02:13 Well, the initials 600, sine of 2 times 20 over 9 .81 meters per second squared.

02:27 That gives me 23 ,588.

02:39 So it's aiming in the direction of the origin, but it's not actually going to strike at the origin because it's going to fly 23 ,58 meters, which is much longer than 5 ,000 meters.

02:55 Okay.

02:57 So this missile is going to go over like this.

03:03 Actually, it's going to still be heading upward when it gets to x equals zero.

03:08 So i need to figure out when it gets to x equals zero.

03:13 So i'm going to use x equals x in.

03:19 Plus v initial t plus one half a x t squared this should be v x as well but this is zero there's no acceleration in the x direction so i wanted to reach zero but it starts at 500 um v initial is in the negative direction that would be negative 600 meters per second times the cosine of 20, to put it in the x direction, times t.

04:03 So i know that i can solve this.

04:07 T is going to be 500 over 600 cosine cosine 20.

04:23 That is the time when it needs, the anti -ballistic missile needs to strike the rocket.

04:33 But at that time, t, the height, which i've called z, is going to be z initial, plus vz initial, t minus one -half g t squared.

04:53 So, z at that point, which i don't know what it's going to be, z initial is zero because the missile was fired from the, the ground, vz initial is 600, sine 20, t minus one half.

05:18 Half of 9 .81 is 4 .905.

05:28 Okay, but we know that t is 500 over 600, cosine 20.

05:35 So z is going to be, just going to put that into a calculator, which i think i have around here somewhere.

05:51 There it is.

05:55 Okay, so 600 minus, nope, 600 20, t minus, what am i looking out here? 4 .905 t squared.

06:28 Okay, but t is 500 .050 .0 .0 .0 .0.

06:33 Over 600 cosine 20.

06:38 T is 0 .8868 seconds.

06:49 Let me write that down.

07:01 That seems awfully fast.

07:06 It's going 600 meters per second for 5 ,000 meters.

07:15 Yeah, that doesn't seem right.