In this lab, we will simulate $($or predict$)$ the behavior of objects$/$systems under different types of force $($i$.$e$.,$ forward

dynamics$).$ Here, note that two different approaches will be used. For problem $1,$ we will solve the differential

equation by ourselves, then use MATLAB to simply plot the solution $($i$.$e$.,$ displacement$).$

Problem $1$ Let's consider a point mass thrown into the air with an initial velocity $v0$ and angle $.$ The goal

of this assignment is to write a MATLAB program that estimates the trajectory of the ball over time and

display necessary information $($using either a graph or some type of animation$).$

The skeleton of the program is provided in the next page. Here, you need to find the equations for the $x$ and

$y$ coordinate of the ball and fill out the portion left blank. $($When executed, this program will ask the user to

input information regarding the movement, including initial velocity and angle, as well as how many

seconds the user wants to simulate the behavior$)*$ You can also change some parameters to make the

animation run faster $($e$.$g$.,$ decrease dt$).$

Lab report preparation $(1)$ Problem $1$

a$.$ Present clearly the calculation process of deriving equations for the $x-$ and $y-$coordinates of the ball.

b$.$ Include the matlab code that you completed and used.

c$.$ Run a few simulations with some parameters of your choice $($initial velocity, initial angle$),$ and draw some

conclusions about how the initial velocity and angle affect the trajectory. Make sure to include some representative

figures to support your conclusion.