The objective of the first problem is to write a MATLAB program that computes and display the path of a projectile for a given initial position (xo, yo), initial velocity (Vo) and initial angle (). See figure below.

Vertical motion The vertical motion is given by ay = -g = 9.81 m/s2 (vertical acceleration) Vy = Voy + ay t (vertical velocity, where Voy: initial velocity in the y-direction) y = yo + Voy t + 0.5 ay t2 (vertical position, yo: initial y-position) t is the variable for time. Horizontal motion ax = 0 m/s2 (acceleration in the x-direction is equal to zero) Vx = Vox (horizontal velocity, where Vox: initial velocity in the x-direction ) x = xo + Vox t (vertical position, xo: initial x-position) Specific initial conditions For this homework we will consider these initial conditions (all Initial position: xo = 0 and yo = 2 m Initial velocity Vo = 15 m/s We are going to consider (simulate) two angles first = 45 deg. and then = 65 deg. For the time variable create a time vector, t, that starts from zero to 3 seconds in steps of 0.01 sec Compute the vertical and horizontal motion. You should divide the MATLAB scripts into different section so it is easier to read. Also, add comments to the variables that you create or the different steps that you are doing. Remember that sin() and cos() functions are for radians and sind() and cosd() for degrees. Note that t is a vector so take care when you need to use exponents for element-by-element. y Vo Vox = Vo cos() Voy = Vo cos() x (xo, yo) = (0, 2) (x1, y1) = (?, ?) coordinates projectile reach max elevation (x2, y2) = (?, ?) coordinates projectile reach ground (y = 0) vertical motion horizontal motion ay = -g = -9.81 m/s2 Vy = Voy + ay t y = yo + Voy t + 0.5 ay t2 ax = 0 m/s2 Vx = Vox (constant value ) x = xo + Vox t t = ? t = ? First simulate the projectile path for = 45 deg. 1a) Plot x-position vs. y-position. Include labels for x- and y-axis 1b) Plot y-position (y-axis) vs. time (in the x-axis). Include labels for x- and y-axis 1c) Plot y-velocity (Vy) vs. time. Include labels for x- and y-axis 1d) Estimate the x and y position and the time when the projectile reach the maximum elevation. (x1, y1) in the figure. You can use the built-in function max 1e) Estimate the x position and time when the projectile hit the ground (when y cross from positive to negative, y0. (x2, y2) in the figure. Note that we dont have any condition to check when the object hit the ground or not. So, the simulation will compute negative position in the y-direction. We will do that later on :) Second simulation = 65 deg. Repeat the simulation but now considering = 65 deg. 1f. Repeat the graphs 1a but now for = 65 deg. 1g. Repeat the graphs 1b but now for = 65 deg 1h. Repeat the graphs 1c but now for = 65 deg (Optional: Note if you want you can include graphs 1a&f; 1b&g; and 1c&h in one graph with different colors and identifying both curves) 1i) Repeat calculation on 1d) but with = 65 deg 1j) Repeat calculation on 1e) but with = 65 deg