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!