HMMT 二月 2000 · 团队赛 · 第 12 题
HMMT February 2000 — Team Round — Problem 12
题目详情
英文原题
- A t a dan e, Abhina v starts from p oin t ( a; 0) and mo v es along the negativ e x dire tionwith sp eed v , while P ei-Hsin starts from (0 ; b ) and glides in the negativ e y-dire tionwith sp eed v . What is the distan e of losest approach b et w een the t w o?ab
解析
英文解析
- A 's p osition is ( a V t; 0) and P 's p osition is (0 ; b V t ). So, at time t , the distan ea b
2 2 qb et w een them is ( a V t ) + ( b V t ) . Noti e that this distan e is the same as thea bdistan e b et w een the p oin t ( a; b ) and the line ( V t; V t ), which is the same as the linea bj Ax + B y + C j
0 0
V x V y = 0. The distan e from a line Ax + B y + C = 0 and ( x ; y ) is ,pb a 0 0
2 2
A + Bj b v a v jso the answ er ispba
V + V22
ba