The Maths and Science Thread - Collection of Problems and Facts

[blake]

1. Half of twelve is seven: how can I be right?

This one wouldn't happen to involve rounding of any type, could it? I seem to remember a similar thing like this where you could claim 2 + 2 = 5, by using the logic 2.4 + 2.4 = 4.8 and then rounding to the nearest whole number...

 

[Kshitiz_Indian]

4. Create a differential equation of motion of the object as it starts falling from rest.

There can be more than one, considering what two quantities you want to relate.

dv / dt = -g

v * dv/dx = -g

Solving the first will give you the relation between the velocity at any point and time, the second will give you the relation between the displacement at any point with respect to the velocity. For a relation between the time and displacement, I guess you could use this -

d^2x / dt^2 = -g

 

[Varun]

Okay two maths problems here:

1. Half of twelve is seven: how can I be right?

2. 62 - 63 = 1

Rearrange one digit one place to make this equation correct. You may not change the mathematical sign or move it. You may not swap two numbers.


Good luck, if you can be bothered that is!

1.) Some higher level I think.
2.) Replace 2 with 3?

 

[drainpipe32]

63-1=62?

 

[Dutch]

1.) Some higher level I think.
2.) Replace 2 with 3?

no you cant swap two numbers with each other....you can only move one number!

dutchad added 0 Minutes and 37 Seconds later...

63-1=62?

Nah...you have moved more than one number....you can only move one numeber

dutchad added 1 Minutes and 37 Seconds later...

This one wouldn't happen to involve rounding of any type, could it? I seem to remember a similar thing like this where you could claim 2 + 2 = 5, by using the logic 2.4 + 2.4 = 4.8 and then rounding to the nearest whole number...

nah it is much easier than that....think simple, very simple!

 

[drainpipe32]

Can we add another sign?

 

[Dutch]

Can we add another sign?

Nientos!

 

[drainpipe32]

Grandchildren?

 

[gudduthemaster]

Yeah all those are pretty darn easy questions. If only something like that came in the IIT's...

keep Dreaming

2. 62 - 63 = 1

1.12=XII
12/2=XII=VII=7
:laugh I miss this Type of Question



2.62=LXII 63=LXIII 1=I
so we can Move only one Number
so

LXIII-LXIII=0 ,I moved that I

 

[Dutch]

keep Dreaming

2^6-63=1

1.12=XII
12/2=XII=VII=7
:laugh I miss this Type of Question


another solution
2.62=LXII 63=LXIII 1=I
so we can Move only one Number
so

LXIII-LXIII=0 ,I moved that I

Well done that man! Did you work it out or "google" it?

 

[gudduthemaster]

Well done that man! Did you work it out or "google" it?

Neither , Found the 1st one in the last Page of Rough book ,and applied the same idea for 2nd one ,[ that 2^6 solution was Completely my idea ]

 

[Dutch]

Neither , Found the 1st one in the last Page of Rough book ,and applied the same idea for 2nd one ,[ that 2^6 solution was Completely my idea ]

Good on you. I do love that kind of question!

 

[Varun]

Another question of reasoning:

A man goes out for a walk. He walks south one mile, east one mile, and north one mile, and ends up in the same place he started. He didn't start out at the north pole -- so where did he?

 

[TumTum]

Another question of reasoning:

A man goes out for a walk. He walks south one mile, east one mile, and north one mile, and ends up in the same place he started. He didn't start out at the north pole -- so where did he?

Equator?

TumTum added 1 Minutes and 11 Seconds later...

There can be more than one, considering what two quantities you want to relate.

dv / dt = -g

v * dv/dx = -g

Solving the first will give you the relation between the velocity at any point and time, the second will give you the relation between the displacement at any point with respect to the velocity. For a relation between the time and displacement, I guess you could use this -

d^2x / dt^2 = -g

Ok but you forgot the force applied by the wind resistance. F=k(v^2)

Hence you cannot solve it using the constant acceleration formulas.

 

[ZoraxDoom]

1. What is the acceleration of a free falling object near the surface of the earth?

9.81 m/s^2


2. If the free falling object (of 64kg) is falling at a constant speed, what is the force applied by the wind resistance?

Constant speed, therefore upward force = downward force. That is, no resultant for or acceleration is acting on the body.
Therefore the wind resistance = weight of the object
= 64 * 9.81
= 627.84 N


3. If the wind resistance coefficient is 4kg/m, what speed is the object falling at?

Don't know the forumlas involved with coefficients of resistance.


4. Create a differential equation of motion of the object as it starts falling from rest.

Resultant force = Weight - Air Resistance

Air Resistance depends on Velocity for one thing, but I don't know what other variable.

dP/dt = mg - dv/dt if I use time for the second variable. So rate of change of momentum = mg - dv/dt, but dv/dt is just acceleration, so *shrug*.


5. Assuming 95% is close enough to 100%, how long will it take for the object to achieve full speed?

Don't think I can solve this without the above parts.

ZoraxDoom added 2 Minutes and 39 Seconds later...

Another question of reasoning:

A man goes out for a walk. He walks south one mile, east one mile, and north one mile, and ends up in the same place he started. He didn't start out at the north pole -- so where did he?

Well, he's 1 mile east of where he started, so unless he started one one of the latitudes or the equator, he can't have ended up where he started