#DON'T CHANGE ANYTHING IN THIS CELL import numpy as np import matplotlib import matplotlib.pyplot as plt %matplotlib inline import pandas as pd

#DON'T CHANGE ANYTHING IN THIS CELL #Method makeplots() plots the data in the dataframe. It makes three line plots #Plot 1: y position vs. x position of the projectile #Plot 2: x (and y) velocities of the projectile vs. time ploted on the same axis #Plot 3: x (and y) acceleration of the projectile vs. time ploted on the same axis def makeplots(): df.plot(x ='x', y='y', kind = 'line', title='Path of Projectile [m]') plt.xlabel('Horizontal Postion') plt.ylabel('Vertical Postion') df.plot(x='t', y={'vx','vy'}, kind = 'line', title='Velocities [m/s] vs. Time [s]') plt.xlabel('Time') plt.ylabel('Velocity') df.plot(x='t', y={'ax','ay'}, kind = 'line', title='Accelerations [m/s/s] vs. Time [s]'); plt.xlabel('Time') plt.ylabel('Acceleration')

#DO NOT CHANGE THE NAMES OF THE METHODS OR THE VARIABLES #THAT ARE GETTING PASSED TO THESE METHODS #Method getaccelerationx has inputs of the current s_y (height) #and the current v_x and v_y. It returns the current value of #the x acceleration. It will call getdensity(height) def get_acc_x(height,vx,vy): # Put your code between the lines #_________________________________________________ #_________________________________________________ return #make sure to return a value here #Method getaccelerationx has inputs of the current s_y (height) #and the current v_x and v_y. It returns the current value of #the y acceleration. It will call getdensity(height) def get_acc_y(height,vx,vy): # Put your code between the lines #_________________________________________________ #_________________________________________________ return #make sure to return a value here #Method getdensity has inputs of the current s_y (height) #and uses the equation for the density of air provided #in the description to return the density at the input height def getdensity(height): # Put your code between the lines #_________________________________________________ #_________________________________________________ return #make sure to return a value here

#DON'T CHANGE ANYTHING IN THIS CELL #NOTICE THIS METHOD RETURNS THE RANGE (THIS WILL BE HELPFUL IF YOU ATTEMPT LEVEL 2) #Method takeshot(v,theta) takes inputs of an initial launch velocity in #(m/s) and launch angle in (degrees)it returns the range of the projectile in (m). #It initialze the data lists and then updates the lists with each timestep. def takeshot(v,theta): # convert angle to radians theta = theta*np.pi/180 #initialize all lists t=0 x=0 y=0 vx=v*np.cos(theta) vy=v*np.sin(theta) ax=get_acc_x(y,vx,vy) ay=get_acc_y(y,vx,vy) data = [[t,x,y,vx,vy,ax,ay]] #make a list of lists #iterate system while (y >= 0 ): # Put your code between the lines #___________________________________________________ #___________________________________________________ data.append([t,x,y,vx,vy,ax,ay]) return data

#ONLY CHANGE THE VALUES OF V AND T IN THE FOLLOWING CODE #this is the main code for level 1 #you have to provide the initial conditions V = speed, and T = theta #it then calls takeshot(v,t) which outputs a big list of lists of all #the data. We then convert that big list of lists into a pandas dataframe #that we can use to view the data or make nice looking plots. V=1600 T= 50 data = takeshot(V,T) df = pd.DataFrame(data, columns = ["t","x","y","vx","vy","ax","ay"]) print('Time of Flight = ',df['t'].iloc[-1], ' seconds') print('Range of Projectile is: ',df['x'].iloc[-1], ' meters') makeplots()

#Method find_optimal_angle() has an input of the initial speed (v) and returns the #the optimal launch angle for that speed and the range of that optimal launch. It #should make use of method takeshot(). def find_optimal_angle(v): # Put your code between the lines #___________________________________________________ #___________________________________________________ return #don't forget to return the optimal angle

#this is the main code for level 2 #it makes a call to find_optimal_angle, which returns an angle #then the range and angle are printed, followed by graphs of #the optimal conditions. V=1600 #set intitial launch speed (R,T)=find_optimal_angle(V) #make call to main method print('Optimal Launch angle is: ', T, 'degrees') #print angle print('Range is: ',R,'meters') #print range makeplots() #make plots