Math trick, an Amazon interview question

[Chenchele]

Critical thinking Vs just I'm good at Mathematics.

 

[dronedrake]

0.00 m

 

[Makanyaga]

View attachment 1360349

Critical thinking Vs just I'm good at Mathematics.

Assuming the cable is inelastic, and that it is symmetrical about its lowest vertical point, the formulae for the path of a trajectory of a projectile motion will solve this. For simplicity of viewing and solving the problem however, you may need to invert the sketch upside down and then find an apparent angle of projection, say alpha (assuming it were a projection). Will come back to you latter

 

[Makanyaga]

View attachment 1360349

Critical thinking Vs just I'm good at Mathematics.

In other words, this question states as follows:

A cable of length 80m hung between two poles, 50m above the ground, has its lowest point 10m above the ground. What would be the length of a similar cable that would have its lowest middle point 50m above the ground, hung between same two poles and at the same height above the ground as the first pole?

SOLUTION:
Cable length 80m is 10m out of a height of 50m; above the ground;
What cable length would have its lowest point 50m above the ground?

Note that as the height of points where the cable is hung increases, the length of the cable decrees. So cable length decreases with the ascent of the points of hanging

Therefore the cable length is
(80x10)/50=16m

Hence; the two poles are 16m apart; Critical thinking Vs just I'm good at Mathematics.

 

[Chenchele]

In other words, this question states as follows:

A cable of length 80m hung between two poles, 50m above the ground, has its lowest point 10m above the ground. What would be the length of a similar cable that would have its lowest middle point 50m above the ground, hung between same two poles and at the same height above the ground as the first pole?

SOLUTION:
Cable length 80m is 10m out of a height of 50m; above the ground;
What cable length would have its lowest point 50m above the ground?

Note that as the height of points where the cable is hung increases, the length of the cable decrees. So cable length decreases with the ascent of the points of hanging

Therefore the cable length is
(80x10)/50=16m

Hence; the two poles are 16m apart; Critical thinking Vs just I'm good at Mathematics.

Not an answer. Good try Mr. 👏

 

[Chenchele]

0.00 m

Great👏. But you have googled it 😅

 

[dronedrake]

Great👏. But you have googled it 😅

aisee

 

[Makanyaga]

Not an answer. Good try Mr. 👏

It's an intepretation of your question, since the question mostly, contained numbers and a geometrical figure. It's the interpretation without which someone cannot easily grasp the correct meaning of the question, thereby causing him to miss the correct answer

 

[Chenchele]

It's an intepretation of your question, since the question mostly, contained numbers and a geometrical figure. It's the interpretation without which someone cannot easily grasp the correct meaning of the question, thereby causing him to miss the correct answer

Yes your right.

And most of mathematicians derived and reached to the same equation but they were stuck to one final equation because the solution resulted the distance between the poles as 0 meter.

They missed physical interpretation that when the distance between the poles is 0 means the poles are close together.

 

[Makanyaga]

Yes your right.

And most of mathematicians derived and reached to the same equation but they were stuck to one final equation because the solution resulted the distance between the poles as 0 meter.

They missed physical interpretation that when the distance between the poles is 0 means the poles are close together.

Solving this problem requires "normal human logic" only, combined with some simple mathematical skills

 

[Makanyaga]

View attachment 1360349

Critical thinking Vs just I'm good at Mathematics.

Hivi kumbe ulikuwa na swali moja tu, hauna mengine si ndiyo? Watu bado wanayahitaji kama maswali bado yapo!

 

[Chenchele]

Hivi kumbe ulikuwa na swali moja tu, hauna mengine si ndiyo? Watu bado wanayahitaji kama maswali bado yapo!

😅😅

 

[Makanyaga]

😅😅

Maswali yako wapi?

 

[Chenchele]

Maswali yako wapi?

Unahitaji maswali ya aina gani Charlie?

design, science, engineering, philosophy, etc?

 

[Makanyaga]

Unahitaji maswali ya aina gani Charlie?

design, science, engineering, philosophy, etc?

Umehama tena kwenye mahesabu? Anyway, kama umehama basi chagua wewe mwenyewe discipline unayopenda kuuliza

 

[Chenchele]

Umehama tena kwenye mahesabu? Anyway, kama umehama basi chagua wewe mwenyewe discipline unayopenda kuuliza

Einstein relativity

Why Einstein concluded that Speed of light is the Universal speed limit?

Based on your understanding and 4D extra imagination, Dou you think that the whole universe which consists of several galaxies which they later consists of planets plus other celestial bodies, there is no where we can find an object moving faster than light?

Think about that,


________

Hints:
According to relativity theories' mathematical results shows that..
"There isn't enough energy in the entire universe to propel just a single electron to the speed of light"

Based on your realized imagination, how is this possible?
🤔

 

[Makanyaga]

Einstein relativity

Why Einstein concluded that Speed of light is the Universal speed limit?

Based on your understanding and 4D extra imagination, Dou you think that the whole universe which consists of several galaxies which they later consists of planets plus other celestial bodies, there is no where we can find an object moving faster than light?

Think about that,


________

Hints:
According to relativity theories' mathematical results shows that..
"There isn't enough energy in the entire universe to propel just a single electron to the speed of light"

Based on your realized imagination, how is this possible?
🤔

Was this second part of your explanations, a hint or a question as well? How many questions are contained here, in your explanations?

When I was in college, I never had a chance of studying cosmology. However I have something for you to see here


Mass of an electron; m_e=9.10938356 × 10^(-31) kilograms

Speed of light; c=299,792,458 m / s

Therefore
Energy E required to be given to an electron so that it can move at the speed of light is:

E=mc^2 (assuming there is no conversion of mass of electron into energy, since at higher speeds (close to that of light), part of mass of a moving object is normally converted into energy)

Therefore
E=(9.10938356 × 10^31)x(299 792 458 m / s )^2=8.19*10^17*10^(-31)=8.19x10^(-14) joules of energy, which is approximately zero. Therefore almost zero energy is needed to propel an electron to the speed of light.

Now how do I go about answering your question, from here? Certainly I'm stuck!

 

[Chenchele]

Was this second part of your explanations, a hint or a question as well? How many questions are contained here, in your explanations?

When I was in college, I never had a chance of studying cosmology. However I have something for you to see here


Mass of an electron; m_e=9.10938356 × 10^(-31) kilograms

Speed of light; c=299,792,458 m / s

Therefore
Energy E required to be given to an electron so that it can move at the speed of light is:

E=mc^2 (assuming there is no conversion of mass of electron into energy, since at higher speeds (close to that of light), part of mass of a moving object is normally converted into energy)

Therefore
E=(9.10938356 × 10^31)x(299 792 458 m / s )^2=8.19*10^17*10^(-31)=8.19x10^(-14) joules of energy, which is approximately zero. Therefore almost zero energy is needed to propel an electron to the speed of light.

Now how do I go about answering your question, from here? Certainly I'm stuck!

First it's Einstein relativity not cosmology

The energy you calculated is a binding energy, the result of nuclear fusion or fission after mass defects

2nd, you have judged electron with single eq E=mc², assumed p=0 which is momentum

3rd, the Energy required to propel a single electron at light speed is not zero, it's infinite energy, there is not total energy in our Earth that can accelerate an electron close to light speed, nor in the whole universe. Only zero mass phenomenon (photos) can and hence moves with light speed.

4th, in relativity, nothing can move at light speed, let alone faster than light speed. Increasing propellant energy? the object mass increases, it's speed slows down and hence gravitational waves accounts here.

5th, you have forgotten to include a Lorentz factor, gamma (y)
Which is;

y=1/√(1-v²/c²)

At rest, electron mass, Mo is constant

In motion, electron mass increases and is given by:

Me=ym
Where Me= mass of electron in motion
y= gamma constant, see it above
m=electron rest mass

Now as you can see, energy of electron in motion, approximated as

E=ymc²

Assuming an electron approach light speed C, then the gamma constant above becomes infinite

Plugging values in E you get infinite joules to propel a single electron at light speed.

__

 

[Makanyaga]

First it's Einstein relativity not cosmology

The energy you calculated is a binding energy, the result of nuclear fusion or fission after mass defects

2nd, you have judged electron with single eq E=mc², assumed p=0 which is momentum

3rd, the Energy required to propel a single electron at light speed is not zero, it's infinite energy, there is not total energy in our Earth that can accelerate an electron close to light speed, nor in the whole universe. Only zero mass phenomenon (photos) can and hence moves with light speed.

4th, in relativity, nothing can move at light speed, let alone faster than light speed. Increasing propellant energy? the object mass increases, it's speed slows down and hence gravitational waves accounts here.

5th, you have forgotten to include a Lorentz factor, gamma (y)
Which is;

y=1/√(1-v²/c²)

At rest, electron mass, Mo is constant

In motion, electron mass increases and is given by:

Me=ym
Where Me= mass of electron in motion
y= gamma constant, see it above
m=electron rest mass

Now as you can see, energy of electron in motion, approximated as

E=ymc²

Assuming an electron approach light speed C, then the gamma constant above becomes infinite

Plugging values in E you get infinite joules to propel a single electron at light speed.

__

Seeing in your explanations here, more of quantum physics (not mentioned in your explanations) than Einstein's theory of relativity. Thanks for you explanations anyway. I may need to update a bit my undergraduate physics or my A-level Physics and Chemistry!

 

[Chenchele]

Seeing in your explanations here, more of quantum physics (not mentioned in your explanations) than Einstein's theory of relativity. Thanks for you explanations anyway. I may need to update a bit my undergraduate physics or my A-level Physics and Chemistry!

Einstein avoided the theory of quantum physics into relativity. Quantum physics is a very challenging physics with lots of theories that are hard to experiment, it's incomplete physics. Saying an electron is a wave and hence a particle, is not it challenging to grasp? Imagine incorporating this wave-particle duality into relativity, then the relativity physics has to be re-written.