HMMT 二月 2002 · 几何 · 第 2 题
HMMT February 2002 — Geometry — Problem 2
题目详情
英文原题
- Dan is holding one end of a 26 inch long piece of light string that has a heavy bead onit with each hand (so that the string lies along straight lines). If he starts with his handstogether at the start and leaves his hands at the same height, how far does he need to pullhis hands apart so that the bead moves upward by 8 inches?
解析
英文解析
- Dan is holding one end of a 26 inch long piece of light string that has a heavy beadon it with each hand (so that the string lies along straight lines). If he starts with his handstogether at the start and leaves his hands at the same height, how far does he need to pullhis hands apart so that the bead moves upward by 8 inches?
Solution: After he pulls the bead is 5 inches below his hands, and it is 13 inches fromeach hand. Using the Pythagorean theorem, his hands must be 2 · 12 = 24 inches apart.