The Maths and Science Thread - Collection of Problems and Facts

[Chewie]

let d be the initial distance. the speed of sound initially is 2d/x.
Next he is d-a from the cliff. The speed of sound is 2(d-a)/y
Rearranging for d gives xv/2=d and yv/2+a=d
Equating these gives xv/2=yv/2+a
Multiplying through by 2 gives xv=yv+2a
Rearranging gives v(x-y)=2a
Dividing through by (x-y) gives v=2a/(x-y) which is the answer

 

[Kshitiz_Indian]

Distance = speed * time

Let us assume the man is d metres from the cliff initially. Assuming the speed of sound to be 'v',

2d = v * x
(2d because sound has to travel the d distance twice before the person hears the echo. This is just distance = speed * time)

Then he moved 'a' metres close. Therefore the distance for sound to travel is reduced by '2a'(this is the critical part), because it has saved 'a' distance in two trips of sound.

2d-2a = v * y

subtract these two equations
2a = v(x-y)

therefore

v = 2a/x-y m/s Hope you got it!

 

[Chewie]

You're much clearer than me lol

 

[Kshitiz_Indian]

I didn't see your post before posting mine, or else I wouldn't have posted! There are many ways to solve a problem though. He's young though, so I thought about choosing the easiest method I could see!

 

[King Cricket]

Wow, it's easy as hell! Guess I unnecessarily got confused while trying to solve it. Thanks to both Kshitiz and Chewie.

 

[Varun]

An easy but interesting one -

We have a cube of volume 1m3 is cut into no. of cubes of volume 1mm3. All these cubes are aligned in a straight row, calculate the length of the row.

 

[Abhas]

hmm..
1 m3 means 1000x1000x1000 mm3 = 1000000000 mm3
since the volume of each small cube is 1mm3, its side is 1mm.

Therefore length of the line should be:
1000000000 mm = 1000000 m = 1000 km!

 

[Varun]

Haha! Isn't it amazing, that with just a 1m3 cube, we can have a 1000 km line?

 

[AkshayC]

questions

1.How can you express the number 100 using six nines and no other digits?
2.If you put a coin in an empty bottle and insert a cork into the neck of the bottle, how could you remove the coin without taking the cork out or breaking the bottle?
3.Why is it better to have round manhole covers than square ones?
4.how can you throw an egg on a concrete without breaking it???

akshaychauhan added 18 Minutes and 2 Seconds later...

sina+sinb+sinc=1
then prove cosa+ cosb+cos c=0

 

[Aussie Team]

1. 9x9+9+9+9/9

2. Simply push the cork into the bottle and shake the coin out.

3. Square manholes can be turned in such a way as to fall into the hole. A circle is the same diameter no matter which way you turn it.

 

[Abhas]

4.how can you throw an egg on a concrete without breaking it???

The concrete is quite hard to break with an egg.

 

[Varun]

The final question is wrong.
It should be sinA + sinB + sinC = 3

 

[Brook]

The final question is wrong.
It should be sinA + sinB + sinC = 3

Why?

 

[Varun]

Why?

If SinA + SinB + SinC = 3, then we have angle A = angle B = angle C = 90 degrees (Since sin90 = 1)
Then cosA + cosB + cosC would 0.

 

[Brook]

If SinA + SinB + SinC = 3, then we have angle A = angle B = angle C = 90 degrees (Since sin90 = 1)
Then cosA + cosB + cosC would 0.

Suppose sinA = sinB = 1, then cos A = cos B = 0 (A = B = 90degrees). But then you could have sinC = -1, and cos C = 0 (C = 270degrees)

Then sinA + sinB + sinC = 1 and cosA + cosB + cosC = 0