📘 related rates, calculus

1. **Problem Statement:** Two planes are flying at right angles to each other, both at the same altitude, converging on a point. One plane is 225 miles from the point, moving at 45

1. **State the problem:** Two planes leave an airport at 1 pm. One travels north at 150 mph, the other west at 200 mph. We want to find the rate at which the distance between them

1. **State the problem:** Two planes leave the airport at 1 pm. One travels north at 150 mph, the other west at 200 mph. We want to find the rate at which the distance between them

1. **Problem statement:** A hot air balloon is rising vertically from a point on a level field. A range finder is located 500 ft from the liftoff point. At the moment when the elev

1. **State the problem:** We have a paper cup shaped like an inverted right circular cone with height $h=6$ inches and diameter $6$ inches (so radius $r=3$ inches). Water is being

1. **Problem statement:** A man walks along a path from a house at 2 m/s. The light is 7 m from the house and 5 m from the path. We want to find the rate at which his shadow moves

1. **State the problem:** We have a triangular trough 10 feet long, 6 feet across the top, and 3 feet deep. Water flows in at 12 cubic feet per minute. We want to find how fast the