A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat at a point that is 1 ft above water level. The rope goes from the bow of the boat to a pulley located at the edge of the dock 8 ft above water level. If he pulls in the rope at a rate of 3 ft/sec, how fast (in feet per second) is the boat approaching the dock when the point of attachment is 12 ft from the dock?

Q: A bright light is sitting on the ground 20 feet from a wall. A 2ft tall dog begins to run from the…

A: The situation can be illustrated with this figure:

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: Given: Since the height is decreasing.     To determine:

Q: A 26 foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 3…

A:

Q: An arc light is hung 12 ft. directly above a straight horizontal wall on which a boy 5 ft. tall is…

A: Given an arc light is hung 12 ft. directly above a straight horizontal wall on which a boy 5 ft.…

Q: "A Kite 65 feet above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle…

A: Given a kite 65 feet above the ground moves horizontally at a speed of 6 ft/s.

Q: A person is holding a kite 5 ft above the ground. The kite gets stuck on a 20 ft tree. As the person…

A:

Q: woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is…

A: SOLUTION-

Q: A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.