## Balloon Drop Problem

 A helium baloon carrying a baseball goes up to a height h feet where it pops and releases the ball. The ball travels the last 3000 feet in 5 seconds. Assume no friction and acceleration due to gravity to be 32 ft/sec/sec. How high was the ball when it dropped? Enter: Enter 3000 feet here Enter: Enter 5 seconds here Answer: V2 - V1 = a*T => 32*5 = 160 ft/sec Answer: V2*V2 - V1*V1 = 2*a*X = 2*32*3000 = 192,000 Answer: V2 + V1 = 192000/160 = 1200 ft/sec Answer: V2 = (1200 + 160)/2 = 680 ft/sec Answer: V1 = V2 - 160 = 680 - 160 = 520 ft/sec Answer: V2 = 8*(SqRt(h)) => h = (V2/8)*(V2/8) = (680/8)*(680/8) = 7225 ft high when dropped

## Horizon Problem

 Fill in the information and then click on button. Enter: Eye Level Height = 5280 feet Enter: Radius of the Earth = 3959 miles Answer: Distance to Horizon = Miles = 88.98876333560322 miles Answer: Distance to Horizon = Feet = 469860.670411985 feet Formula used here: Let d*d = 2*R*h + h*h => d = SqRt(2*R*h + h*h) R = 3959 miles h = 30/5280 miles This is distance to tangent of circle! When d = 89 miles you will notice that h = 1 mile! So every time you travel 89 miles you should drop 1 mile because of the curve of the earth! => C = 2*Pi*R = 24875 miles => 24875/89 = 280 pie slices => if you traveled 1/4 of the circle = 6218.75 miles => 280/4 = 70 pie slices (each a mile drop) => 70 mile drop which cannot be right. Since 1/4 of the circle would result in a drop of the Radius = 3959 miles? Rule of thumb approximation: Let h = eye level height = feet Nautical miles d = 1.17*(SqRt(h)) 1 N.Mile = 6076 feet and 1 S.Mile = 5280 feet Enter: Distance in Miles = 89 miles traveled Enter: Radius of the Earth = 3959 miles Answer: Height = Miles = 1.000505305742081 miles Answer: Height = Feet = 5282.6680143181875 feet Formula used here: Let h*h = R*R - d*d => h = SqRt(R*R - d*d) R = 3959 miles d = 12 miles This is distance from chord to circle! Enter: Drone Height = 50 feet Enter: Radius of the Earth = 3959 miles Enter: Height of Sun at sunset = .5 degrees Answer: Distance to Horizon = miles Answer: Speed of Sun = Miles per 3 minutes Answer: Speed of Sun = Feet per Second Answer: Speed of Sun = Miles per Hour This is Feet per Second Straight Up!