# A skew throw
#
# made by: Gustav Frederik Heide Siegfried
#          Mahdi Al-Helw
#          Ming Hui Sun
#
# date: 20. feb. 2019.

#Definition of variables
g = 9.82
x0 = 0
v0 = 300
y0 = -0.46
#Definition of vectors
x_values_one = c()
x_values_two = c()

#A for loop to go through all angels between 0 and 90
for (v in 1:90){
v = (v*(pi/180))

#Calculation of possible solutions (intersection of the x-axis)
a = -0.5*g
b = v0*sin(v)
c = y0
d = b^2-4*a*c
#Evaluating the discriminate for possible solutions
if (d > 0) {
#Calculating the t for the two solutions (x(t))
t_one = (-b - sqrt(d)) / (2*a)
t_two = (-b + sqrt(d)) / (2*a)
#Calculating the value of x at the intersection of the x-axis
x_one = (v0 * cos(v) * t_one + x0)
x_values_one = c(x_values_one,x_one)

x_two = (v0 * cos(v) * t_two + x0)
x_values_two = c(x_values_two,x_two)
} else {
  break
}
}
#Finding the best angles, by finding the one with the higest x value
best_angle_one = which.max(x_values_one)
best_angle_two = which.max(x_values_two)
#Plotting all of the angles with their x_max, with both solutions
plot(x_values_one,type="l", xlim = c(0,90), ylim = c(x_values_two[1],x_values_one[best_angle_one]),
xlab="Angle",ylab="x_max",main=paste("The best angle for the positive solution is:",best_angle_one,"The best angle for the negative solution is:",best_angle_two, sep="\n"))
lines(x_values_two,col="black")
segments(0,0,90,0)
segments(best_angle_one,0,best_angle_one,x_values_one[best_angle_one])
segments(best_angle_two,0,best_angle_two,x_values_two[best_angle_two])