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Thread: Playing with Math...

  1. #21
    Gold Member Dave S's Avatar
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    Here's one for the physics folks...

    A ship sails straight from point "a" to point "b" across the ocean, it covers a distance of 3000Kms in 150Hrs, and it's average speed is 20Knt, however the actual distance from "a" to "b" is only 2500Kms and the ship's velocity is 16.667Knt, explain how this is possible?
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    Email problem vieome's Avatar
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    Quote Originally Posted by Dave S View Post
    Here's one for the physics folks...

    A ship sails straight from point "a" to point "b" across the ocean, it covers a distance of 3000Kms in 150Hrs, and it's average speed is 20Knt, however the actual distance from "a" to "b" is only 2500Kms and the ship's velocity is 16.667Knt, explain how this is possible?
    The ship moves on a zig zag course from a to b

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    Email problem vieome's Avatar
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    Not so much maths or english the following, but more to make one think, I think!

    Why doesn't Tarzan have a beard when he lives in the jungle without a razor?


    Why do we press harder on a remote control when we know the batteries are flat?


    Why do banks charge a fee on 'insufficient funds' when they know there is not enough?


    Why do Kamikaze pilots wear helmets?


    Why does someone believe you when you say there are four billion stars, but check when you say the paint is wet?

  4. #24
    Gold Member Dave S's Avatar
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    Quote Originally Posted by vieome View Post
    The ship moves on a zig zag course from a to b
    Yes, but not in the way we imagine a zig-zag motion. The ship sails STRAIGHT from "a" to "b" means it did not zig-zag (left to right), but rather followed the motion of the waves, zig-zag up and down, therefore accounting for it's extra travel distance.
    Today Defines Tomorrow
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  5. #25
    Gold Member Dave S's Avatar
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    Quote Originally Posted by vieome View Post
    Not so much maths or english the following, but more to make one think, I think!

    Why doesn't Tarzan have a beard when he lives in the jungle without a razor?


    Why do we press harder on a remote control when we know the batteries are flat?


    Why do banks charge a fee on 'insufficient funds' when they know there is not enough?


    Why do Kamikaze pilots wear helmets?


    Why does someone believe you when you say there are four billion stars, but check when you say the paint is wet?

    Funny old world we're in...
    Today Defines Tomorrow
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  6. #26
    Site Caretaker Dave A's Avatar
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    Quote Originally Posted by tec0 View Post
    It is seemingly obvious that Velocity = Displacement/Time and that Speed = Distance/Time yet there is a condition where Velocity = Speed... The exception that proofs the rule? Maybe... [It is easy you don't have to google it ]
    As much fun as Dave S's answer was, the simple answer is when the object is stationary - i.e. both distance and displacement = 0
    QED

    p.s. - on the North Pole one, you have to go due South, then Due East (or West), then due North to end up at your original point. Take a 90% angled turn at each point and you'll end up (approximately - curve of earth hurts a little bit here) 5km due South of the North Pole.
    Essentially the difference between an equilateral triangle and a square, the angles matter - even at the North Pole.

  7. #27
    Gold Member Dave S's Avatar
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    Quote Originally Posted by Dave A View Post
    As much fun as Dave S's answer was, the simple answer is when the object is stationary - i.e. both distance and displacement = 0
    QED

    p.s. - on the North Pole one, you have to go due South, then Due East (or West), then due North to end up at your original point. Take a 90% angled turn at each point and you'll end up (approximately - curve of earth hurts a little bit here) 5km due South of the North Pole.
    Essentially the difference between an equilateral triangle and a square, the angles matter - even at the North Pole.
    On the first question, you are right, this is the second case where velocity=speed.
    On the north pole one, I will concede that the instruction to turn left (right) by 90 deg. is misleading, and should have been "turns 90Deg. and walks Due East (West)" would have been better.

    However, when one does turn through a given angle on the earth's surface and then walks a straight line, that straight line is actually going to follow the curvature of the earth, to demonstrate this. If you were to walk "in a straight line" toward the East, from the point you are now (Durban assumed?), logically you would (at some great future date) arrive back at the point where you started? Physically, however, this is not the case and you would carry on walking, until (eventually) you would arrive at the South Pole. The same would be true if you were using a compass. But if you used GPS co-ords, you would make it back to where you started (your walk line may not be straight). This is simply the effect of the magnetic attraction (or lack thereof?) of the poles. There is one place on earth where one can walk in a straight line, East or West, and arrive at their exact starting point without GPS Co-ords, and without a compass (provided you can maintain a straight line?). Does anyone know where this is?

    PS. Hint, It does depend on the time of year, and the continent you start from. Don't forget the 23Deg. axis inclination (centreline of orbit in relation to the sun).
    Last edited by Dave S; 17-Jul-13 at 07:08 AM. Reason: Added PS.
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  8. #28
    Diamond Member tec0's Avatar
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    Quote Originally Posted by Dave S View Post
    Only if an object is travelling at a constant speed, in a straight line, in a constant direction, without effect of acceleration/deceleration, between points "a" and "b", can it be said that the object velocity = the object speed. In such a case displacement would be equal and we now only require to calculate the distance/time.

    Picture in your minds eye, a bullet fired from a gun, when the bullet leaves the muzzle of the gun, this is the last point where the velocity and speed of the bullet are equal. As the bullet loses momentum so it begins to fall to earth, thereby changing it's direction and its displacement, eventually the bullet will stop at some point. A straight line to that point [where the bullet landed] is the displacement (or the distance the bullet has moved away from the gun), divide this by the time it took for the bullet to get there, equals the VELOCITY of the bullet. Now imagine the full arc that the bullet has travelled, (or the distance the bullet has travelled), divide this by the time it took for the bullet to get there equals the SPEED of the bullet.
    Sounds about right... Funny thing is I knew you where going to use the bullet example... Now if only I can figure out the lotto numbers
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    Email problem vieome's Avatar
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    Quote Originally Posted by tec0 View Post
    Sounds about right... Funny thing is I knew you where going to use the bullet example... Now if only I can figure out the lotto numbers
    3 15 17 19 21 47

  10. #30
    Gold Member Dave S's Avatar
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    Quote Originally Posted by tec0 View Post
    Sounds about right... Funny thing is I knew you where going to use the bullet example... Now if only I can figure out the lotto numbers
    Strange you should mention the lotto numbers, I've always had the correct numbers in every draw since 2001, problem is they keep drawing the wrong numbers...
    Today Defines Tomorrow
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