Possible Correction for Graded Assignment 2 (Q3)

[nibedita chakraborty]

Sir,

In this question tan(theta) is 2/3 which is a positive value and all other straight line, example :- SM (m= -0.66), SN (m= -0.73), SL (m= -0.61), SK (m= -0.56) have negative slope. In this case all the workers should be safe. It will be very kind of you to reevaluate this question.

Thanking you.

Yours sincerely

Nibedita Chakraborty   

[IITM Student]

I strongly agree here. I see everyone is assuming that the shot was fired downwards? Where is it mentioned? Why should we assume anything if there is no information. I had intentionally changed my answer to "All are safe" because as per the information available (and without assumption), the ballet will go upwards. 

On Tuesday, October 27, 2020 at 10:46:38 AM UTC+4 harish...@gmail.com wrote:

If we take the equation of path of bullet using point slope formula we get: y/2-x/3=30. The X-axis co-ordinate of M is 82. Substituting in the equation we get y=87.3.

i.e. the bullet passes through the co-ordinate (82,87.3) which is much higher than the head of M. Thus proving person M is safe.

So option should be: All workers are safe.

[IITM Student]

*bullet may go upwards.

 I am not questioning other things like - can it pass body or if it hits at foot or if bounces. First task is to find - the line or direction bullet is traveling based on available data.

[harish...@gmail.com]

Yes if value of tan θ was -2/3 then bullet would have clipped M at (82,2.66). Since it's a positive value then all should be safe.

[sayantan bagchi]

yes i think the value should be -2/3

[Potato]

Please read the question carefully.

 the question also mentions this piece of data

"  Since the range covered by the bullet is short, the path of the bullet is assumed to be a straight-line path.  "

If the bullet was fired with a positive slope of 2/3 in the air, there is no chance of it following a straight path. It will have to follow a - 'up and then ultimately, a parabolically-down' path.

This straight line path can occur only if the bullet was fired straight down.

A similar problem was solved in one of the lectures, where the value of slope was +ve, but while solving it, the instructor explained how he converted it to a -ve slope by taking (180- theta)

[sayantan bagchi]

[sayantan bagchi]

he may have convert. But this is an ambiguous statement.

[harish...@gmail.com]

A bullet fired upwards will go straight for a short duration as well. Assumptions can only be taken from the data and here, no where it's said that the bullet was fired down. Instead it's clearly given in the question that tanθ is positive 3/7

[Potato]

Hi Harish

I do not mean to disregard your point of view, instead i'm just clearing mine out

Two things:

1.   "Since the range covered by the bullet is short, the path... " The question talks about the complete range of the bullet and doesnt say half of the trajectory is straight.

2. The question just gives the value of  tanθ and not doesnt explicitly state it to be the slope of the trajectory. It further clarifies that θ is the angle made by the bullet wrt to the horizontal

PFB an image depiction to make it more clear

[harish...@gmail.com]

I understand your point and it's correct. But even if the bullet is fired upwards the question still becomes relevant. 

[Potato]

I know what you mean. But if we were to consider an upwards travel, the sentence  "Since the range covered by the bullet is short, the path... "  will make no sense and the question would be totally meaningless. 

That is just an interpretation of mine.

There's nothing wrong in you trying to get your voice out. I support your actions but i dont think they are going to change their minds as they have already uploaded the solutions PDF

Again, dont get me wrong. You might be correct, but im not the one to decide. :)

Cheers

[Debojyoti Basu Majumder]

No the point is that, if they wish to not answer our queries and clarify an ambiguous question, then IIT Madras has no authority to run this course where students' genuine doubts are unanswered.

[IITM Student]

I understand almost everyone assumed this to get the answer. I also did same but then when I read again, I didn't see it mentioned anywhere.

I can assume- Point saying it's straight distance is to highlight that  we should think it's a straight line. Assumptions are endless-  can't there be any object in slightly upwards direction stopping it and making it short distance? Why we have to assume short distance is just  because it's falling on the ground. Isn't it common to have buildings taller than 60 feet at some distance which will make it short distance? What is definition of short distance? I take this only to say we are talking about straight line for all our calculations.

Point here is question is not clear. Students are able to answer only based on assumption. Remember - we are studying computers which depend mostly on input and it's very important to make clear statements.

[harish...@gmail.com]

Now that you explicitly point it out that might be correct. I'm not hoping for a change instead clarification from the faculty team would be great. 

But you do have a valid point though.

Cheers  

[subhajit POD]

Hi all, 

This is Subhajit from the course support team. I have read all the comments you made above. 

At first you have to remember that this is a contextual question and to answer this you have to apply the common sense ( which is going to be really important through out the course ) as you have seen in the tutorial videos where we have given some examples of problem solving which were of similar types. 

Secondly in this question the workers are standing downwards so is there any point of shooting the bullet in the upward direction (even if the bullet was misfired)? I think that does not make sense. Even if we assume the bullet is fired in the upward direction with some inclination with the horizontal, at some point its vertical velocity will become zero and it will follow a parabolic path afterwards. So in this context that does not really make sense. 

Now in the question  it is given that the angle of the path of bullet makes with horizontal is theta, where tan (theta) is given to be positive. So its safe to assume that theta is an acute angle ( the other possibility is the angle is greater than 180 degree and less than 270 degree, clearly we can ignore this case). Now if we consider the angle of inclination of the path followed by the bullet, then as the bullet is fired downward it is clear from the diagram that the angle of inclination is obtuse angle , let it be alpha. So the theta which is given here must be  (180-alpha) degree. 

The details solution is already uploaded in the portal, please check for the further details. 

Hope this helps to clarify your doubts. 

Best

Subhajit 

[harish...@gmail.com]

Thank You for the clarification Sir.

[Dhiman Sengupta]

Hi,

I have already gone thru the explanation but can you please take a look and let me what was wrong here (attached herewith),

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Thanks,

Dhiman Sengupta

Bangalore

Ph: +91 7338130710

[subhajit POD]

When the bullet is hitting L according to your figure, observe that the bullet is hitting M first then piercing through him it will hit L, which is assumed to be not possible in reality. As the bullet should change its path after hitting one person depending on the speed of the bullet and many other factors, which are not mentioned anywhere in the question. So we are assuming that the bullet stops after hitting one person, we have discussed in many threads of the discussion forum and in live sessions also. 

Hope it clarifies your doubt. 

Best

Subhajit

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[subhajit POD]

Hi Kaushik, 

Please go through the solution properly, the slope is taken to be negative there. When theta is defined to be the angle of inclination then it is taken anti-clockwise with respect to the positive  X-axis. tan of that angle of inclination is defined as the slope. Please take a look at the additional lecture 3 uploaded in week 2 content. 

Hope it will clear your doubts. 

Now regarding your doubt about the firing upward, I was saying that if it is fired upward with some inclination then at some point the vertical velocity will be zero and then due to gravity the bullet should follow the parabolic  path. So it is not possible for the bullet to follow the whole trajectory as the st. line. 

Hope this helps. 

Best

Subhajit

On Tue, Oct 27, 2020 at 4:06 PM Kaushik Deka <linka...@gmail.com> wrote:

Dear Subhajit,

The solution provided in the answer key assumes that the sniper misfired the bullet in the downward direction and so tan(theta) = - 2/3 is taken, while tan(theta) = 2/3 is given. The real confusion is that tan(theta) is defined as dy/dx, and is conventionally taken as negative only if one of the directions (x or y) is negative in the cartesian plane. So, for tan(theta) to be positive, both the distances must be positive => equation of the bullet's trajectory (assuming straight line) must be y = (2/3)x + 60 with x-intercept = - 90 , y-intercept = 60; and NOT y = - (2/3)x + 60 with x-intercept = 90 ( if the workers are to right side of the sniper as shown) ! Regarding the trajectory of the bullet, it is explicitly mentioned that it follows a straight line owing to its short ( undefined distance ) range, so why will common sense make anyone assume parabolic trajectory ? Also, why will the sniper MISFIRE in the direction of the workers - against common sense! 

The bigger concern though is the inherent subjectivity and implicit focus on rote learning observed in the assignment problems. I have learnt that objectivity is a critical tenet of the scientific method. So, this being a BSc degree in data science, undermining objectivity and promotion of traditional memorization techniques will consequently undermine the development of robust quantitative reasoning necessary for solving real-world problems.

Look forward to further clarification.

Regards,

Kaushik

[subhajit POD]

The explanation does not depend on the personal perception. The angle theta must be acute angle as tan is given as positive. But when we are seeing that the bullet is fired towards the workers  then the slope must be negative. So angle of inclination is nothing but (180-theta).

Please check the additional lecture 3 uploaded in the portal for clarification on angle of inclination and slope. 

Best

Subhajit

On Tue, Oct 27, 2020 at 4:31 PM <vedsha...@gmail.com> wrote:

Dear Subhajit,

I don't think it is about common sense because the topic discussed here is slopes and lines. Regarding your explanation- if it is fired in the upward direction.. at some point it's vertical velocity will become 0 and it will come down. , what happens when it hits the ground, will it continue in straight-line (if straight-line is the key point here to assume straight-line is possible only in downward direction, after hitting the ground also it will not continue in straight-line. Is "short" fixed time? because definition of short time will change depending on  where the bullet hits the ground. In fact bullet will most probably travel in straight line for longer time if fired upwards (if no obstruction) compared to time it takes to hit the ground. 

 As it says it will continue straight- we can assume it will continue straight in  upward direction as well. It's not right to expect us to manipulate our thinking, to match what the person who made the question paper was thinking. A simple word mentioning direction would have helped here. Or are we expecting that the main point is reaching a decision if it is downward or upward?

We might think straight-line is mentioned just to clear that all the calculation are done using formulas for line and we don't go in direction that bullet can not travel perfect straight (which makes sense).

These explanations are just personal perception. which might defer from person to person and the ambiguity remains there. Was this done on purpose to check logic/ common sense?

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[Balachandra k]

Hi assuming it is coming down towards prisoners but how can we tell it will not pierce. Because if it pierces it would have gone to 90ft and hit L's feet

so L is in trouble along with M

bullet stopping should have been clearly mentioned in Q

many times we may have missed live sessions

On Tuesday, 27 October 2020 at 18:29:15 UTC+5:30 linka...@gmail.com wrote:

Hi Subhajit,

I have posted my question after going through all the lectures and solution keys from week2. Tutorial 8 problem is almost similar but since it is not schematically specified whether the thieves are to right or left of Sanya's balcony, one can arrive at the given answers without any contradiction w.r.t. slope of torchlight, by rearranging the relative positions of Sanya and the thieves. But, if you consider the torchlight directed upward, which would be contextually absurd in that problem, you will arrive at a different solution.

However, in Q3 (elaborating my interpretation for clarity) :

1) The schematic explicitly specifies the relative positions of sniper and workers - workers are to the right of the sniper ( if you flip the positions, the given solution will be correct without conflict w.r.t. given tan(theta)! )

2) The bullet's trajectory is assumed to be a straight line - even if initial velocity becomes zero at some point in the +ve x-direction, there is no reason to assume that this will happen within the relevant range i.e. <= 96 ft -  'short' is not defined ! 

3) Theta is the angle made with the horizontal & tan(theta) = 2/3 => theta ~ 33.69 degrees measured anti-clockwise from +ve x-axis !  

So, from 1) , 2) & 3), the bullet's trajectory MUST be y = (2/3)x + 60 and NOT y = - (2/3)x + 60 as given in the solution key. Then the correct solution should be: all are safe !

Now, where am I wrong ?

Hope I am able to articulate the issue. Rough work is attached herewith.

Sincerely,

Kaushik

[Big Endian]

Hello Subhajit,

The reasons you cite are not satisfactory at all.

It is one thing to say the bullet is (mis)fired at an angle theta to the horizontal - in which case the angle could be made above or below the horizontal, and it is quite another when it is explicitly said that the slope, that is the tan(theta) is 2/3, a positive real number. Once tan(theta) is mentioned as a positive real number, there can be very little ambiguity on the angle.

Also, it will help to find the equation of the trajectory of the bullet, put it in y = mx + c form and see if m is really positive.

In the end we're humans, we all make mistakes. The least one can expect from IITM is to be fair, accept and correct them when they are made.

Thanks.

[nibedita chakraborty]

Sir, 

I am highly obliged that you answered the query so resourcefully. But unfortunately still some doubts persists, it will be very kind of you to answer them as well.

Firstly, I strongly agree that the bullet cannot be fired upward since after a point it will for sure follow a parabolic trajectory and that bullet cannot pierce a body (M in this case) and hit another (L in this case).

Thus I would like to share my ideology of this problem (how I solved it), I would be grateful if you could say if it is correct or not.

Please see the attached file (my rough work)

According to my diagram the black line represents the line which should have been assumed to get the answer as given in the solution. Here as you have said if we measure the angle anti-clock wise we get (180-theta), therefore getting a negative slope and a st.line.

But, also the orange line represents my ideology. The line makes an angle theta with the x-axis anticlock-wise only. But the bullet is fired downward not upward thus maintaining the concept of the question (since in the question the bullet is supposed to follow a st.line trajectory the direction it goes in should not determine the slope of the line). 

In the Tutorial which has the similar kind of problem, there changing the sign (+ve or -ve) has meaning since the thieves could be on either side of the building (as the girl is not supposed to know where the thieves are), this was an trial and error question (we where supposed to check with both positive and negative slope).

But unlikely in this case we should not be changing the slope of the line since the bullet can be misfired only in one direction at a time.

Hope this rough work and explanation is clear. I will be eagerly waiting for your reply.

Thank you.

Your sincerely

 Nibedita Chakraborty

[manu kumar]

Hi Subhajit,

    Assumptions are subject to persons thinking style or the way one sees the world. Quite frankly this course is not improve or test ones assumption power. If you assume it'll stop after hitting M then you may have some grounds to believe it similarly, those who think it'll penetrate also have their own grounds to think that way. You cannot enforce your assumptions to be common sense or generic to everybody. If these many thread have questioned your assumption then you should rethink if your assumption is 100% right. This is a Maths assignment not ballistics science.  "the bullet is hitting M first then piercing through him it will hit L, which is assumed to be not possible in reality." -> Can you make a ballistic expert say this. It is easy to say this as you are the decision maker but can't be reality.  If common sense needs to be applied thoroughly then my questions would be what are these people doing just standing strictly straight to their height? are they humans or mannequins? what about possibilities of one sitting or scratching his leg for a flee bite. Why can't we assume these too? aren't these practical situations? it has more reality than yours. I agree assignment are suppose to test ones ability solve mathematical problems and be good at it. I don't understand why assumptions are being given higher priority here and getting tested? Not happy with the responses with words like 'Common sense', 'Your assumption is the reality and no other". For god sake in English subject you are teaching importance of 'Listening' too. Understand other perspectives too. I'm saying penetrating or not penetration both are possibilities. People should be given marks in both cases.

Regards

Manu B       

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Dhiman Sengupta

Bangalore

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[Goutam Basu]

Please see the attachment. It's very simple & straight forward without going much deeper onto it.

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[Devendra Govil]

I strongly disagree with this assumption that a bullet can't hit two bodies together. 

If one were to come to the specifics of the case, any decent sniper rifle, has enough power to probably go through 3 or more bodies at a distance of around 10m. 

Remember a Sniper Rifle is built to be lethal at a range of ~1km. It will easily go through 2 people at a distance of around 10m.

The common sense and scientific assumption in fact is that the bullet can go through multiple people. 

If you are not convinced, I will have to calculate the momentum requirements and prove that it will be able go through 2 bodies. 

[manu]

Yes, focus should b on Nov 22. Now everyone should b sharp on their common sense. This is hidden 5th subject of the course. Thing is we dont get to debate on such questions from qualifiers. Thos who fail or miss their target mark by couple of marks knows the importance of this thread.

[Dhiman Sengupta]

I concur with you. Based on the available data, our task was to identify who were in the risky zone. Why are we bringing some assumptions in a mathematical problem that one bullet will stop after hitting say X or Y.  Not sure, we are putting more stress on someone's perception, assumption or any other cognitive skills. 

Many times we read in the paper, one bullet just touches someone's body and hits the next person who was in that direction. I feel, we should not consider such conditionswhile solving any math problem.

    

On Tue, Oct 27, 2020 at 10:39 PM manu kumar <manu...@gmail.com> wrote:

[Goutam Basu]

Please refer to the attachment. It was already clarified on 22 Oct that Bullet will not damage anyone after 1st hit.

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[Dhiman Sengupta]

Very true Manu..

[manu]

Hi Gautam,

 

     After common sense and assumptions test. Now, you are expecting everyone to follow some threads to solve the given problem. Wah.. if you see people asking such doubt why was that clarification not made as an announcement? Isn't it your responsibility? 

On Wed, 28 Oct, 2020, 1:34 am Kaushik Deka, <linka...@gmail.com> wrote:

P.S. - The given solution is unequivocally wrong because slope of bullet path = - tan(theta) = - 2/3 is taken just to validate the assumption of the person who solved it. This objectively violates the given constraint that slope of bullet path = tan(theta) = 2/3. Negativity of linear gradient essentially arises from directional mismatch of measurements in the cartesian plane, not from 'negative' measurement of the angle. Sign (+/-) of angular measurement is but a convention to justify the sign of slope i.e. rise or fall in the cartesian plane. So, slope is alway tan(theta) and tan(theta) may turn out to be negative by conventions of cartesian geometry, not because of clockwise measurement of the angle. So, it is conventionally wrong to state that slope = tan(-theta) = - tan(theta) ! 

Say, the given solution for Q3 is correct. 

Then, by cartesian conventions :

slope of bullet path = tan(theta) = (0-60)/(x-intercept-0) = - 60/x-intercept  ----- (1)

Given, tan(theta) = 2/3 ------ (2)

From (1) & (2), if x-intercept is positive, then - 60/x-intercept is never = 2/3

Hence, the assumption that the bullet is misfired in the downward direction is wrong.

However, - 60/x-intercept = 2/3 will only hold if x-intercept = -90

=> the bullet is misfired at an angle +(theta) from the horizontal !

Otherwise, the conventions of cartesian geometry will have to be rewritten to validate one's assumptions ! :)

Regards,

Kaushik

[Abhighyan Sinha]

Completely agree with you. We cannot be expected assume a different value for a clearly given value, that also violates the fundamental conventions of geometry.

Though unrelated to this, but in case of the bullet piercing one or more than one person, students should not be compelled to follow all the posts in the forum. Either the facts should be clearly stated in the question, or in the very least further clarifications should be mailed to us.

On Wednesday, October 28, 2020 at 1:34:19 AM UTC+5:30 linka...@gmail.com wrote:

P.S. - The given solution is unequivocally wrong because slope of bullet path = - tan(theta) = - 2/3 is taken just to validate the assumption of the person who solved it. This objectively violates the given constraint that slope of bullet path = tan(theta) = 2/3. Negativity of linear gradient essentially arises from directional mismatch of measurements in the cartesian plane, not from 'negative' measurement of the angle. Sign (+/-) of angular measurement is but a convention to justify the sign of slope i.e. rise or fall in the cartesian plane. So, slope is alway tan(theta) and tan(theta) may turn out to be negative by conventions of cartesian geometry, not because of clockwise measurement of the angle. So, it is conventionally wrong to state that slope = tan(-theta) = - tan(theta) ! 

Say, the given solution for Q3 is correct. 

Then, by cartesian conventions :

slope of bullet path = tan(theta) = (0-60)/(x-intercept-0) = - 60/x-intercept  ----- (1)

Given, tan(theta) = 2/3 ------ (2)

From (1) & (2), if x-intercept is positive, then - 60/x-intercept is never = 2/3

Hence, the assumption that the bullet is misfired in the downward direction is wrong.

However, - 60/x-intercept = 2/3 will only hold if x-intercept = -90

=> the bullet is misfired at an angle +(theta) from the horizontal !

Otherwise, the conventions of cartesian geometry will have to be rewritten to validate one's assumptions ! :)

Regards,

Kaushik

On Wednesday, October 28, 2020 at 12:20:19 AM UTC+5:30 bas...@gmail.com wrote:

[prasanth PS]

Hi All,

let us all go through the given answers for the question. The below are the options.

1. All workers are safe.

2. All the workers are safe except K.

3. Only K and N are safe.

4. No one is safe.

5. Only K is safe.

6. All the workers are safe except M.

If we need to consider the bullet will stop after hitting a person either it need to mention in the question as a condition or the given optional answers should not give any confusion regarding this perception or one announcement need to be provided by the team. . The given optional answer no: 3,4 and 5 are directly hitting our common-sense that, the bullet will pass through the body after hitting a person. Either it need give the clarification in the question or it should not give the optional MCQ's which is directly clarifying this query.

Moreover somebody was mentioning in the forum that, there a was query regarding this question before submission, and it got answered by the team that " Bullet will not disturb any other person once it hit a person". Please note that, thousands of queries flying in this forum in a daily basis. either it need to mention in the question or an official mail from the concerned team was required these type of corrections.

rgds,

Prasanth.

[IITM Student]

Kaushik has put the point - what I was trying to make using proper terms.  [ As we expected to use common sense and logic, why we are not using logic that we are 3 D world means, sniper, N, M L, K might not be straight line]]

About the explanation from Graded assignment solution: 

I did not think about the -if K and L and are safe because as per the given data bullet was going upward which meant everyone is safe. Now - the solution says that KL and are safe because after hitting M ,bullet won't travel further. Fine. What is definition of "safe". I would say- only when we are 100 % sure that bullet is not going to hit the person, we consider it safe. If we apply common sense and logic, (as it was expected to conclude that bullet is fired downwards),there is no 100 % chance that bullet is going to hit M (the real world is 3 dimension, the bullet's angle towards ground might be passing at height lower than  height of M but is M's position not be in that line, but either K or L might be in line. So even if we apply the angle logic, we can't say that K and L are safe just because the bullet might hit M (as there is no 100 % chance). Although I see that bullet will hit ground at 90 feet (position of K), do we consider that safe? May be if you say for the sake of this question ..but you can't say K is safe as the bullet has hit (again applying 3 D world logic, M might or might not be in line).

Now- you might say 3 D is not part of topics taught. Same way gravity and the reason provided that angle is upward is also not part of the curriculum. So do you want us to apply logic and common sense for one part (that too to match your assumption) and don't apply logic about real world which doesn't even require you to know concept of gravity and parabolic trajectory. If someone fires from height at y2 not everyone in (360 degree) is at risk, on the person in line ( remember 3 D world)

[Nikunj Rabadiya]

Greetings

Subhajit Sir,

I read mostly all chat about Bullet questions, One of your explanations - "Bullet would go after anywhere after hitting first person it depends upon the velocity of the bullet, angle, etc.." (on this argument nobody safe )

I am okay with the argument of yours. But it's wouldn't necessary to mention like fatal, injured - like this keyword used than your argument kind of satisfied. But in question asked who was not safe! 

safe mean anything like - bullet won't do any damage that particular person. 

but as here assumption made bullet stop after hitting 1st person.

Too much ambiguity,

My main concern in future, how to deal with this type of question?

Regards 

Nikunj 

[Balachandra k]

I strongly agree penetrate or does not penetrate how can we assume. We assumed that it will penetrate as it says who all are safe. So the chances of penetrating are high. The Question is wrong and since so many have confusion, then better marks is awarded for the Question to all as the overall performance of students can come down and which is not completely their mistake

[Kaushik Deka]

I have deleted my previous comments as it seems questioning a subjectively biased decision of the admin is a complete waste of time in this forum. But, do conclude that such questions would be appropriate as MSQ reather than as MCQ. That way, subjective assumptions would not gain priority over objective reasoning in a scientific study of mathematics.

Best,

Kaushik