8Vectors and Motion
In 1872, capitalist and former California governor Leland Stanford
asked photographer Eadweard Muybridge if he would work for him on a
project to settle a $25,000 bet (a princely sum at that time). Stanfordís
friends were convinced that a galloping horse always had at least one foot
on the ground, but Stanford claimed that there was a moment during each
cycle of the motion when all four feet were in the air. The human eye was
simply not fast enough to settle the question. In 1878, Muybridge finally
succeeded in producing what amounted to a motion picture of the horse,
showing conclusively that all four feet did leave the ground at one point.
(Muybridge was a colorful figure in San Francisco history, and his acquittal
for the murder of his wifeís lover was considered the trial of the century in
The losers of the bet had probably been influenced by Aristotelian
reasoning, for instance the expectation that a leaping horse would lose
horizontal velocity while in the air with no force to push it forward, so that
it would be more efficient for the horse to run without leaping. But even for
students who have converted wholeheartedly to Newtonianism, the rela-
tionship between force and acceleration leads to some conceptual difficul-
ties, the main one being a problem with the true but seemingly absurd
statement that an object can have an acceleration vector whose direction is
not the same as the direction of motion. The horse, for instance, has nearly
constant horizontal velocity, so its a
is zero. But as anyone can tell you who
has ridden a galloping horse, the horse accelerates up and down. The horseís
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