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The distance between the base of the ladder and the wall, x, and the height of the ladder on the wall, y, represent the sides of a right triangle with the ladder as the hypotenuse, h. The objective is to find dy / dt , the rate of change of y with respect to time, t , when h , x and dx / dt , the rate of change of x , are known.
A quartic equation has four solutions, and only one solution for this equation matches the problem as presented. Another solution is for a case where one ladder (and wall) is below ground level and the other above ground level. In this case the ladders do not actually cross, but their extensions do so at the specified height.
The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
An extension ladder. A ladder is a vertical or inclined set of rungs or steps commonly used for climbing or descending. There are two types: rigid ladders that are self-supporting or that may be leaned against a vertical surface such as a wall, and rollable ladders, such as those made of rope or aluminium, that may be hung from the top.
The ladder frame is for a person sitting on the front of the ladder, with x ′ and t ′ being the ladder space and time axes respectively. The blue and red lines, AB and AC, depict the ladder at the time when its front end meets the garage's exit door, in the frame of reference of the garage and the ladder, respectively.
In the mathematical field of graph theory, the ladder graph L n is a planar, undirected graph with 2n vertices and 3n – 2 edges. [ 1 ] The ladder graph can be obtained as the Cartesian product of two path graphs , one of which has only one edge: L n ,1 = P n × P 2 .
The problems associated with this paradox can be applied to any other conflict between two abstractly defined extremes that are opposite. One of the answers generated by seeming paradoxes like these is that there is no contradiction – that there is not a false dilemma. Christopher Kaczor suggested that the need to change indicates a lack of ...
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.