The worlds first riddle!

Where's the ruling on the speeder?

Oh yes, I knew there was something else I had to attend to today.



Original question:
Mark is driving his sports car traveling at 40 m/s (144 km/h) he passes a police car hidden behind a billboard. Two seconds after the car passes the billboard the police car is on the road accelerating at 3.0 m/s squared.

How long will it take the police to catch this somewhat careless speeder?

Mark: "28.53567 seconds"

Try writes, "May I respectfully suggest a review of your speed may be beneficial."

Mark replies;
In two seconds, Mark will be 80m past the cop.
Mark's distance function is 80+40t
The cop's distance function is 1.5t^2
The cop will catch Mark when 1.5t^2 = 80+40t
1.5t^2 - 40t - 80 = 0
Using the quadratic formula:
t = [40 +/- sqrt(1600 + 480)] / 3
t = [40 +/- sqrt(2080)] / 3
Since sqrt(2080) > 40
t = [40 + sqrt(2080)] / 3 = 28.53567


"I stand by my answer"

I, after a swig of moonshine retort, "Let battle be joined on the morrow."

Mark then replies via the Supreme Court "Bring it on, baby!"


Therefore, dear reader this is the current situation, lines have been drawn in the sand, alliances forged. Whilst it is possible we could both be wrong, it is all too clear, we both cannot both be right. Perhaps Ralph was right all along.

In a world where to the victor goes the sponsorship and glory, whilst the vanquished held to ridicule, and forced to live in a cave.
The question remains; how may this impasse be resolved?

The first step would be to show your answer and how it was derived.

Fair point. Ok, enough of this tension building flip flopping. Put up or shut up, that's my motto. Well, here goes…

t0 = 2s for speeder

ds = 40 m/s to + 40 m/s t
dp = 3.0 m/s2 (t)2
ds = dp
40 (2) + 40t = 3.0t2
3.0t2 - 40t - 80 = 0

t = 40 +/- (1600 + 4(3)(80))1/2
= 15.1, -1.77 time always (t)

It will take the police 15.1 s to catch the speeder.

Or will it?

d = a/2 * t^2
not
d = a * t^2

Ok, ok, that is an error any six year old could make. Let it be known throughout the land I hold no grudge, or ill will against anyone for making me out to be such a dork. I am just thankful Ralph was not right. :wink:

Double or quits?

A van travels a maximum of 100 km/h. Its speed decreases in proportion with the number of passengers. The van can carry a maximum of seven people. Given that the van can travel 88 km/h with three people in the van, what will be the speed of the van when six people are on board

Egg: Spin the egg on the flat surface. A hard boiled egg spins smoothly and rapidly. A raw egg does not.
Sorry for the delay on this, even though I have already read the answers to LIFES MYSTERIES, I will still submit my answers.
Grain
focal length
sound

[size=8]VAN
Is that 100 km/h with a driver or empty?

100 km/h with driver: 70 km/h
100 km/h without driver: 76 km/h

HOUSES
The width of the rope.[/size]

OMG we agree - tiebreak:


Two cars race around a circular track, in opposite directions, at constant rates. They start at the same point and meet every 30 seconds. If they move in the same direction, they meet every 120 seconds.

If the track is 1800 m long, what is the speed of each car

[size=8]CARS
37.5 m/s
22.5 m/s[/size]

And now the end is near, and so I face the final curtain,
Mark my friend, I'll say it clear,
I'll state my case, of which I'm certain.
I've lived a life that's full, I travelled each and every highway,
And more, much more than this, I did it my way.

Regrets I have a few, but then again, too many to mention,
I did what I had to do, and saw it thru' with one exception,
I planned each chartered course,
Each careful step along the by-way.

Yes there were times, I'm sure you knew,
When I bit off more than I could chew,
But thru' it all, when there was doubt,
To say the things one truly feels,
And not the words of one who kneels,

I've loved, I've laughed and cried,
My share of losing, and now, as tears subside,
Let the record show I took the blows.
And more, much more than this, I did it my way.



Let that be a lesson to all - DO IT MARK'S WAY ~

Mark:

EGG
A hard boiled egg can be spun like a top. A raw egg can't.

VAN

100 km/h with driver: 70 km/h
100 km/h without driver: 76 km/h

100 - 3t = 88
100 - 88 = 3t

t = 12/3
t = 4 km/h reduction in speed per person

When six persons are on board, the van travels at
100 - 6t = 100 - 6(4) = 76 km/h



HOUSES
The width of the rope.

Damn ~ The houses are zero metres apart. This is a problem that people with too much mathematical knowledge (could) get mixed up with, because they start thinking of the equation of a freely hanging rope - a catenary - which is quite complicated, and they forget that a drop of 5 metres means the rope also rises 5 metres. (although some don't) Now since we only have a 10 metre rope, the rope must hang straight down.

CARS
37.5 m/s
22.5 m/s

Let x = rate of car 1 (m/s)
Let y = rate of car 2 (m/s)



(1) 1800m = 30x+30y
1800-30x = 30y
7200-120x = 120y (2) 1800 + 120x = 120y

Solve for Car 1: (1)=(2)
7200-120x = 1800+120x
5400 = 240x
x = 22.5 m/s

Convert to km/hr
x = 22.5m/sec *60sec/min*60min/hr = 81 km/hr
1000 m/km


Solve for Car 2:

Substitute x = 22.5 m/s

1800+120x = 120y
y = 1800+120x
120

y = 1800+120(22.5)
120

y = 37.5 m/s

Convert to km/hr
x =37.5m/sec *60sec/min*60min/hr = 135 km/hr 1000 m/km




The South will rise again ~ ~ ~ in the meantime I think I will go to the restroom…

Take a roll of toilet paper Stuff a fat pen in the center of the cardboard tube so that the writing point is dead center. Lay the toilet roll on the floor next to a wall, and give in a little push. The toilet roll will unroll and the pen will draw some sort of shape on the wall.

What is the figure the pen draws

[size=8]TOILET PAPER
Without having done any calculations (if the answer isn't posted today, I try it tonight), I'll say a parabola (until the paper runs out; then it's a horizontal line).[/size]

Pen and toilet roll: It will draw an increasing radius spiral

In 1897 three French Balloonists tried to reach the North pole. Balloons, of course, can only travel with the wind, but they planned to overcome this problem by adding sails to their balloon, which would allow them to sail across and into the wind like a sailing ship does. Although there was plenty of wind.

Why weren't they successful

Balloon: No. they were not successful. My guess heck yes, is that the balloons can only travel on and with the air current. (I'm still trying to gigure out how sail boats work

Ralph, I appreciate asking a guy in the desert such a question, is like asking a Hillbilly the contents of a Waldorf Salad. How about:


At an interview at a2k towers where you are applying for a job as a moderator, you are given a cup of coffee, it is too hot to drink. To cool it fastest should you (a) leave it undisturbed on the table, (b) blow on it or (c) stir it with the supplied plastic spoon

Coffee: Leaving the coffee on the table undisturbed would allow the heat to stay longer. Blowing on it will only cool the surface briefly. Using the plasitic spoon will allow the temperature to be altered trhough out the cup there for it would cool quicker.

[size=8]BALLOON
A boat is in water which provides friction to keep the wind from turning the boat/sail so that it travels parallel to the wind.

A balloon has no such medium to provide that friction; so the wind will just rotate the balloon and force it to travel parallel to the wind.

COFFEE
(a) is out.
(b) would cool the surface, but convection would cause the cooled surface liquid to mix with the warmer liquid below.
(c) would bring more of the liquid in contact with the air (aids convection), but also adds (negligible) heat due to friction. A metal spoon would probably be better as it would act as a heat sink.

I'll go with (c) since the aid to the natural convection should be beneficial.[/size]

Mark takes the train downtown at completely random times. Because the train he catches follows a circular route, he can take one going west which arrives on the hour or one going east at 20 past and still arrive downtown, so he takes whichever one arrives first. Over a long period of time he finds that he takes the west-going train twice as often as the east-going train.

Is he right in concluding that the transit company must have twice as many trains running west as compared to running east, past his stop