HMMT 十一月 2009 · 团队赛 · 第 5 题
HMMT November 2009 — Team Round — Problem 5
题目详情
英文原题
- [ 3 ] How many times does the ball bounce before it returns to a vertex? (The final contact with a vertexdoes 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
英文解析
- [ 3 ] How many times does the ball bounce before it returns to a vertex? (The final contact with a vertexdoes 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 itdirectly 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.