#====================
# Figure 9.11.R.
# R script to calculate and graph
# projectile motion (such as
# throwing a baseball).
#====================
#---------------------------------------------------------------
# Input initial velocity, angle, and height, in USA common units.
#---------------------------------------------------------------
mph=75          # Initial velocity, miles per hour.
angle=45        # Initial angle, degrees.
height=5        # Initial height, feet.

#---------------------------------------------------------------
# Convert units to meters and seconds.
#---------------------------------------------------------------
v0=mph*1609.344/(60*60)  # Convert velocity to meters per second.
theta=2*pi*angle/360     # Convert angle to radians.
y0=height/3.2808399      # Convert height to meters.
g=9.80665                # Gravitational acceleration constant.

#---------------------------------------------------------------
# Calculate maximum time of flight using quadratic root formula.
#---------------------------------------------------------------
a=-g/2
b=v0*sin(theta)
c=y0
t.max=(-b-sqrt(b^2-4*a*c))/(2*a)  # Max. time of flight.
x.max=v0*cos(theta)*t.max         # Max. distance

#---------------------------------------------------------------
# Plot height at time t vs distance at time t.
#---------------------------------------------------------------
t=t.max*(0:50)/50  # Range of t values between 0 and t.max.
x=v0*cos(theta)*t
y=y0+v0*sin(theta)*t-g*t^2/2
plot(x,y,xlab="distance in meters",ylab="height in meters")  # Plot.
t.max        # Print t.max.
x.max        # Print x.max