P*******b
发帖数: 1001 | 1 puzzle - 2 trains traveling in opposite direction, bird starts from one and
reaches other and flies back and forth like this till train collide. Find th
e time taken to collide, total distance traveled by the bird, and no. of tim
es bird makes a U turn. |
s*****t
发帖数: 737 | 2 V_tr = the speed of trains
V_b = the speed of bird
S = the initial distance between two trains.
The time to collide t = S/(2*V_tr)
The total distance of bird = V_b*t
The distance between the two trains when the bird makes the first U turn is:
S1=S-2*S*V_tr/(V_tr+V_b)=S*(V_b-V_tr)/(V_tr+V_b)
let r=(V_b-V_tr)/(V_tr+V_b)
The distance between the two trains when the bird makes the second U trun is:
S2=S1*r=S*r^2
So the number of times bird makes a U turn is m, where
S*r^m < size(a bird)
This should
【在 P*******b 的大作中提到】
: puzzle - 2 trains traveling in opposite direction, bird starts from one and
: reaches other and flies back and forth like this till train collide. Find th
: e time taken to collide, total distance traveled by the bird, and no. of tim
: es bird makes a U turn.
|
h**k
发帖数: 3368 | 3 the number of bird making u-turn should be infinite.
The distance bird flying each time is a sequence becoming closer to 0 and
can not reach 0 if time and distance can be divided infinitely.
is:
is:
【在 s*****t 的大作中提到】
: V_tr = the speed of trains
: V_b = the speed of bird
: S = the initial distance between two trains.
: The time to collide t = S/(2*V_tr)
: The total distance of bird = V_b*t
: The distance between the two trains when the bird makes the first U turn is:
: S1=S-2*S*V_tr/(V_tr+V_b)=S*(V_b-V_tr)/(V_tr+V_b)
: let r=(V_b-V_tr)/(V_tr+V_b)
: The distance between the two trains when the bird makes the second U trun is:
: S2=S1*r=S*r^2
|
s*********t
发帖数: 1663 | 4 isn't this a typical mistake of limit?
【在 h**k 的大作中提到】
: the number of bird making u-turn should be infinite.
: The distance bird flying each time is a sequence becoming closer to 0 and
: can not reach 0 if time and distance can be divided infinitely.
:
: is:
: is:
|
s*****t
发帖数: 737 | 5 You should not ignored the size of the bird, which means the distance can
not be divided infinitely.
【在 h**k 的大作中提到】
: the number of bird making u-turn should be infinite.
: The distance bird flying each time is a sequence becoming closer to 0 and
: can not reach 0 if time and distance can be divided infinitely.
:
: is:
: is:
|
