Answer:
CODE
import time #importing time module
import math #importing math module
pi = math.pi #defining the value of pi
u = 70 #initial velocity
g = 9.8 #gravitational acceleration
time_step = 0.01 #time step of 0.01 secs
time_elapsed = 0.0
maxAngle = 0
angle = 1
h = 5.0 #setting the initial height to to 5m
x = 0.0
maxRange = 0.0
for angle in range(1,91): #loop which angle takes value from 1 to 90
ux = u * math.cos((pi / 180) * angle) #velocity in x axis
uy = u * math.sin((pi / 180) * angle) #velocity in y axis
for i in range(1000): #running for 1000 steps
dragx = 0.5 * 1.225 * 1.4 * 0.8 * ux * ux #calculating the drag in x direction
dragy = 0.5 * 1.225 * 1.4 * 0.8 * uy * uy #calculating the drag in y direction
drag_ax = dragx / 65.0 #calculating drag acceleration in x axis
drag_ay = dragy / 65.0 #calculating drag acceleration in y axis
accelx = drag_ax #resultant acceleration in x axis
accely = g + drag_ay #resultant acceleration in y axis
vx = ux - accelx * time_step #velocity in the x axis at any instant
vy = uy - accely * time_step #velocity in the y axis at any instant
h += uy * time_step - 0.5 * accely * time_step * time_step #height at any instant of the projectile
x += ux * time_step - 0.5 * accelx * time_step * time_step #range at any instant in the x axis of the projectile
print("Height " + str(h) + " Range " + str(x)) #printing the current position
time.sleep(time_step) #waiting for 0.01 secs
time_elapsed += time_step #calculating the time elapsed
ux = vx #setting the final velocitites to new initial velocities
uy = vy
if h <= 0.0: #if a height 0 is reached
if x > maxRange:
maxRange = x #max angles are noted
maxAngle = angle
h = 5.0 #variables are initialized
x = 0.0
u = 70.0
vx = 0.0
vy = 0.0
print("Wait till the next simulation starts.....")
time.sleep(10.0 - time_elapsed) #wait for 10 secs
time_elapsed = 0.0
break
print("The optimum angle for for Callista is {} degrees which will give her a range of {} metres".format(str(maxAngle),str(maxRange))) #the optimum angle is printed
Explanation:
