ruby physics example

#!/usr/bin/ruby

# example using problem 4.28 from Halliday Physics book
# ••28 In Fig. 4-34, a stone is pro-jected at a cliff of height h
# with an initial speed of 42.0 m/s directed at angle u0 􏰀 60.0° above
# the horizontal. The stone strikes at A, 5.50 s after launching. Find
# (a) the height h of the cliff, (b) the speed of the stone just before
# impact at A, and (c) the maximum height H reached above the ground.

class Fixnum
	def to_rads
		self * Math::PI / 180;
	end
end

if __FILE__ == $PROGRAM_NAME

	# given variables
	velocity_i = 42; 	# m/s
	theta_i = 60; 		# degrees
	time_f = 5.5;		# s
	
	# find
	h_max = nil;
	h_final = nil;
	v_final = nil;
	
	# lemma variables
	velocity_iy = Math.sin(theta_i.to_rads) * velocity_i;
	gravity = -9.8; 		# m/s^2
	
	# equation of motion
	# v_f^2 = v_i^2 + 2g(r_f - r_i)
	# => 0 = velocity_iy^2 + 2 * gravity * h_max
	h_max = -velocity_iy**2 / (2 * gravity);
	puts "Maximum height is: #{h_max} m";
	
	# r_f - r_i = v_i * t + 1/2*a*t
	h_final = velocity_iy * time_f + 0.5 * gravity * time_f**2;
	puts "Final height is: %.2f m" % #{h_final};
	
	v_final = Math.sqrt( (velocity_i * Math.cos(theta_i.to_rads))**2 + (velocity_iy + gravity * time_f)**2);
	puts "Final Velocity is: %.2f m/s" % v_final;
		
	# Output:
	###########
	# Maximum height is: 67.5 m
	# Final height is: 27.35 m
	# Final Velocity is: 27.35 m/s	
end