Jumping Explained.

Dear Editor:
	Mr. Miller’s theory of jumping on other planets is sound physics, but the technique of jumping is not so simple as he assumes. On Earth, a good high jumper can clear six feet. But no man can reach anything like that height standing up. If a man six feet tall clears the bar at six feet, he does so horizontally. Only his feet (no pun intended) rise six feet. His head does not rise at all, and his center of gravity is lifted only about three feet. This three feet is all he actually jumps, and it is all that is affected by gravity; the rest is simply a question of his own height.
	Thus on the Moon, with one sixth the Earth’s gravity, he could clear 3X6+3=21 feet.
	In the broad jump, the vertical velocity cannot be equal to the horizontal, because the latter has been worked up by a long run, and the jumper has no means of converting the one velocity into the other. Photos show that a broad jumper clearing twenty-four feet reaches a height of about six feet, but, like a high jumper, by doubling up his body. In fact, while the distance depends on the height, the height is more or less independent of the horizontal speed. In the broad jump, a man goes nearly as high as in the high jump.
	Then, on the Moon, our broad jumper—assuming he takes off at the same speed as on Earth—will reach a height of about twenty-one feet. As Mr. Miller shows, if his horizontal speed equaled his initial vertical, his distance would be four times his height. But we have seen that it is greater. As altitude varies as the square of the speed, his horizontal speed will be about 1.4 times his initial, increase of forty-four percent in height (120/100 squared=144/100) Thus the Lunar pole-vault record should be about one hundred and thirty-five feet!
	If a sprinter’s strides are ten feet on the Earth, they would be not much more than three feet on Jupiter, so that he would be really walking. As he could not take many more strides a second than on Earth, his speed would be about one third of what he could make on earth. Or, say, eight miles an hour. At this speed, and allowing for gymnastics, the Jovian broad-jump record would be about five or six feet, the pole-vault record about the same.—Charles A. Baker, Jr., Bound Brook, N. J.