How to approach difficult problems?

[Government$]

Hello physics forum.
In last couple of weeks i have been working more difficult problems from Algebra and things are going a bit more difficult where solution is not apparent right away. So i need to spend some time doing one problem until i find a solution. That can be from half an hour to hour or two for one problem. That is not very fast progress and i feel sometimes like i am loosing time and that i am not productive. So the question is how much time should i spend on solving a problem before i check solution at the end of the book? That's how i solve problems from physics. I don't try first alone rather i go straight to the answers and the try to understand problem. I know, that is not a good way of developing my problem skills, because there is going to be time when there won't be an answer at the end of the book and then what? So should i spend hours trying to figure out one problem or after some time i should look for the answers? I usually need a start and after that i can finish a problem by my self.

Thank you

 

[emailanmol]

Hey, I can understand the dilemma you are in.

The first step towards better problem solving is knowing the concepts well.

I would request you to go through your textbooks again to understand the chapter clearly if you haven't done so.

After that, sit alone and start asking yourself what have you learned uptil now.Ask yourself frequent why and how questions.

Your theory should be so strong that you should be capable enough to explain the concepts to others.

Once your theory has been made strong problem solving will get easier.(Certainly!)

The next step is that whenever you read a problem, think about it for sometime.
Usually people start writing equations immediately which is not a right way to do esp in physics(and also in math).

Thinking will help you realize what the question actually wants.

Like let's see a simple example of calculating the range of a projectile.

Most students will immediately start writing the equation of motion( and they may get the answer.But it won't happen always and definitely won't help in time management as the difficulty level increases)

The method is to ask yourself is how the particle is moving.what you need to find the range.

The particle is moving like a curve and
You need the horizintal velocity the horizontal acceleration and the time.

Now obtaining horizintal velocity and acceleration is a one step process.
However , obtaining time is not a one step process.

It would require you to think that the time taken will be equal to the time taken by the particle to go up, stop and then come back to the lowest point.(which can be done only if you can visualise the problem)
After this you can start writing the equations to get this.
(that is think first and then write equations and not vice-versa)

(I hope you are aware of kinematics so that this example helps you.)

This is a simple example i sighted which may seem obvious (if you have studied kinematics).

However as the problem gets tougher, those who think at the basic level correctly and effeciently, are usually those who able to adapt and figure out solutions easily and effeciently as the difficulty level increases :-)

Hope this helps

 

[cgk]

Imo, the best way to learn to solve difficult problems is to learn to solve (i) simple and (ii) medium difficulty problems first. Some books have excercises which are ordered according to difficulty (especially some dedicated exercise books; i.e., not textbooks), with the complexity rising slowly but steadily from task to task, and featuring multiple excercises viewing the same topic and solution strategies from different angles.

For me this was an immensely effective way of getting a routine in standard approaches (which is required to solve difficult problems). If you think that you are not efficient in handling the excercises in your current way, then this may well be true. In that case I highly recommend to look for other textbooks/exercise books which are closer to your way of working: Different approaches work differently for different people, and not all books contain good excercises (in fact, excercises in textbooks are often very poor). Just stop by your local library and look through different books to see what works for you.

 

[Hobin]

Tadaah!

 

[emailanmol]

Hobin, that's an excellent link :-)