You watch at a horizontal distance of 40 ft as a hot air balloon rises straight in the air at 10 ft/s. The balloon has a rope 30 ft long dangling below it. How fast is the balloon moving away from you just as the rope leaves the ground? To receive full credit on this problem, you must sketch a labeled diagram.

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 19 knots and ship B is sailing north at 20 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)   A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole? A circle is inside a square.The radius of the circle is increasing at a rate of 5 meters per minute and the sides of the square are decreasing at a rate of 1 meter per minute.When the radius is 5 meters, and the sides are 16 meters, then how fast is the AREA outside the circle but inside the square changing?