HMMT 十一月 2009 · 团队赛 · 第 5 题

HMMT November 2009 — Team Round — Problem 5

[ 3 ] How many times does the ball bounce before it returns to a vertex? (The final contact with a vertex does not count as a bounce.) Now a ball is launched from a vertex of an equilateral triangle with side length 5. It strikes the opposite side √ after traveling a distance of 19.

解析

[ 3 ] How many times does the ball bounce before it returns to a vertex? (The final contact with a vertex does not count as a bounce.) Answer: 5 Every segment the ball traverses between bounces takes it 7 units horizontally and 2 units up. Thus, after 5 bounces it has traveled up 10 units, and the final segment traversed takes it directly to the upper right vertex of the rectangle. Now a ball is launched from a vertex of an equilateral triangle with side length 5. It strikes the opposite side √ after traveling a distance of 19.