Magical Rectangle
The length and width of a magical rectangle each suddenly begin growing. The length is growing at a rate of 9 ft/s and the width is growing at a rate of 4 ft/s. There is a moment that the length and width are respectively 100 feet and 50 feet respectively. At what rate is the area of the rectangle increasing?
The Third Baseman’ Perspective
A baseball diamond is 90 ft square. There are runners on first and second. The batter hits an infield ground ball which is thrown to third base for a force out. The third baseman then sees the batter running to first at TK ft/s. How far is the runner from the third baseman after he’s run 48′ towards first base? At what rate is the distance between the runner and the third baseman increasing at this same moment? From the third baseman’s perspective, at what rate, in radians-per-second, is the angle between the runner and home plate changing at this same moment?
TK
Conical water tank