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| Author | Creative Math Problems Challenge |
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win again? there was no riddle. lol
No mate, this is the opposite - anyone, who wishes to participate, sends me problems/riddles. I select the best and give prize :) | | + | This is quite a famous one.
Nice and neat, but I've added a bit of a twist to it for those looking for more challenges :)
>> Problem set <<
Suppose 2 trains, A and B, are 30km apart. They both move at 5km/h towards one another.
There's a bee in front of train A that moves to train B at the speed of 20km/h.
(All speeds are with respect to the ground)
Once the bee hits train B, it turns back and moves to train A, still at the speed of 20km/h.
The bee keeps moving so between trains A and B until the 2 trains collide... and the bee is squashed!
>> Prompt <<
Find the total amount of distance traveled by the bee.
Assume that the bee take 0 time in making a turn when it hits the train.
. . Challenge 1 (calculus involved):
Formulate an integral equation for the motion of the bee and verify this with the solution you get above.
Hint: start with v = ds/dt
(v velocity, s distance, t time)
. . Challenge 2 (getting more technical):
Suppose we want to have the computer solve this problem iteratively.
Take each time the bee hits the train and make a turn to be 1 journey.
We start with the distance left to go d= 30km
As the number of journey increases, d decreases, and we want to sum up the distance traveled by the bee.
What fraction of d (the distance left) is covered by the bee after each journey?
What fraction of d is the new distance left between A and B after each journey? | | New Week :) | A solution to my previous submission can be found here:
https://www.lordswm.com/photo_pl_photos.php?aid=225120
This week's submission:
Another nice one, but this time, we need a bit of Physics.
This is not expected out of this thread so I'll just include it at the end, this is for completeness as well.
>> Problem Set <<
Suppose there's an escalator (esc) with n steps and is moving up with speed u (steps per second).
Bob is at the bottom of the esc and walks up along with it. He walks with speed v (same unit as u) with respect to the esc, and by the time he reaches the top, he took 45 steps in total.
Jack is at the top of the esc and walks down against it. He walks with 3 times the speed of Bob, and by the time he reaches the bottom, he took 90 steps in total.
>> Prompt <<
Find n.
>> Preliminaries <<
• Relative Speed
Suppose there's a moving object on a moving platform. If they both move in the same direction and the object moves at speed v with respect to the platform. Then if you are also on that platform, you'll see the object moving at speed v.
But if the platform moves with speed u (with respect to the ground now), and you are outside of it. Then you'd see the object moving at speed v + u.
With respect to the ground, the speed of the object is complemented by the speed of the platform it is on.
[Hint] What happen to the displacement of the object on that platform? Is it also relative with different observers? | | + | | + | Choose a number
Add 5
Multiply 7
Add 3
Multiply 3
Multiply 3
Add all digits of ur ans till it becomes a 1 digit number
Your ans will be 9 | This question will require knowledge on differentiation, anti differentiation and optimisation.
-PART 1-
Vehicle A is 25km due east of vehicle B. A moves due west at 60km/h and B moves due north at 80km/h.
(a) Find an expression for the distance of separation, s for the two vehicles t hours later.
(b) After how many minutes is this separation distance a minimum and what is this minimum required?
-PART 2-
The distance of separation between 2 cars increases 4% every minute, and the vehicles have an initial s of 10km.
(c) Using the info, form an equation relating 'ds/dt' and 's'.
(d) Hence, form an equation relating s and t, based on (c)
(Hint: Euler's number is quite handy here)
(e) After some time, they were 19km apart, what minute did this happen? Round the answer to the nearest minute.
(Hint: logarithm can help calculate unknown indices) | | nice ones here :) | | + | | + |
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