At an athletics hall, there is usually a track for the 60-meter dash. It also has a starting line for a 50-meter dash with respect to the same finish line.
In training, we wanted to run 30 meters, but there was no line for that.
What is the minimum number of additional lines that need to be added so that every distance
{10,20,30,40,50,60} meters can be run on this track?
The track is a straight. It currently has a 0 m line, a 10 m line and a 60m line.
The distances don't have to end at the usual finish line; they can also take any other line as start or finish.
All lines have to be between the 60-meter start and finish line.
@wolfgang59 saidCorrectumundo!
@joe-shmo
A 40m line.
I'm tapping out for the night. I'll dig up some more tomorrow!
@eladar said"Perhaps people around here were not smart enough to figure that out."
So I gave the probability the slower person wins lol.
I thought that is what you were asking.
Perhaps people around here were not smart enough to figure that out.
This statement is odd? Of course I suspected that is what you had done. Please elaborate why I should have given you credit ( and spoiled the unsolved puzzle ) for providing the complimentary probability to what was asked?
Identical balls are released simultaneously along fixed tracks A and B from the left end. ( the beginning's and ends of the tracks are at the same position horizontally and vertically. The tracks are smooth and continuous. The illustration I have attempted does not perfectly represent that )
What is the result of the race? A wins, B wins, or A and B tie?
Assume that the balls roll without slipping. Ignore frictional losses of energy.
Track A:
…\___________/
Track B:
…\__...………__/
………\____/
Four runners ( A,B,C and D) participate in a race.
A,B,C,and D were the runners 1st through 4th place runners.
The runners in 1st and 4th places make TRUE claims.
The runners in 2nd and 3rd make FALSE claims.
The claims made by each of the racers are as follows:
A - "I finished the race after C"
B - "I am the 3rd place runner"
C - "I am not the 4th place runner"
D - "I finished the race before B"
What places did the runners finish?
@joe-shmo saidd,b,c,a
Four runners ( A,B,C and D) participate in a race.
A,B,C,and D were the runners 1st through 4th place runners.
The runners in 1st and 4th places make TRUE claims.
The runners in 2nd and 3rd make FALSE claims.
The claims made by each of the racers are as follows:
A - "I finished the race after C"
B - "I am the 3rd place runner"
C - "I am not the 4th place runner"
D - "I finished the race before B"
What places did the runners finish?
@joe-shmo saidIt is clear that B lies. So he has to have finished second.
Four runners ( A,B,C and D) participate in a race.
A,B,C,and D were the runners 1st through 4th place runners.
The runners in 1st and 4th places make TRUE claims.
The runners in 2nd and 3rd make FALSE claims.
The claims made by each of the racers are as follows:
A - "I finished the race after C"
B - "I am the 3rd place runner"
C - "I am not the 4th place runner"
D - "I finished the race before B"
What places did the runners finish?
C can only be true if he finished 1st.
Then we would have 1. C, 2. B, then D has to have lied and thus finished 3rd and A spoke truth and finished fourth.
But if D spoke truth it would be 1. D, 2. B. A speaking truth would still be fourth and C would have spoken untruth and finished third.
So I find that there are two Solutions.
Since Joe said that the second solution is wrong I go for 1. C, 2. B, 3. D, 4. A
@joe-shmo saidIt must depend where the tracks are located.
Identical balls are released simultaneously along fixed tracks A and B from the left end. ( the beginning's and ends of the tracks are at the same position horizontally and vertically. The tracks are smooth and continuous. The illustration I have attempted does not perfectly represent that )
What is the result of the race? A wins, B wins, or A and B tie?
Assume that t ...[text shortened]... e frictional losses of energy.
Track A:
…\___________/
Track B:
…\__...………__/
………\____/
If one track is at the top of a mountain for instance the gravity would be less so the ball on that track would travel faster
@venda saidThe tracks are located right next to each other. I mentioned the vertical and horizontal positions of the beginning and end are the same. I guess Ill further stipulate that the tracks do not change elevation enough to experience any apreciable change in the force of gravity.
It must depend where the tracks are located.
If one track is at the top of a mountain for instance the gravity would be less so the ball on that track would travel faster
@joe-shmo saidSo this is probably an Energy balance Problem. I the beginning both balls have Zero velocit, but are accelerated by the difference in potential Energy:
Identical balls are released simultaneously along fixed tracks A and B from the left end. ( the beginning's and ends of the tracks are at the same position horizontally and vertically. The tracks are smooth and continuous. The illustration I have attempted does not perfectly represent that )
What is the result of the race? A wins, B wins, or A and B tie?
Assume that t ...[text shortened]... e frictional losses of energy.
Track A:
…\___________/
Track B:
…\__...………__/
………\____/
E(pot)=m*g*dh
This Energy is converted into kinetic Energy
K(kin)= 1/2*m*v^2
At teh end of the track the kinetic Energy is converted back into potentila energy.
So we can consider the identical parts as being identical, the Question is what happens in the middle. In case A the velocity stays constant in case B we have a furzer acceleration by the second portion of potential Energy and a decelartion at the end of that way.
Even if there is some additional way for the second step we can safely assume that track B is run through fast than case B (without friction)