Hello. I am first year student, taking introductory physics course and next week I have a whole-semester exam. (kinematics, dynamics, rigid body, termodynamics, mechanical waves - that kind of basic stuff).

I don't have a chance to directly ask my teacher following questions, so I figured who else could know better but you guys. :)

I am dealing with fairly simple tasks. (you can view my post history to get the idea)

Often, in the task's description, the initial velocity is ##v_{i} = 0##, or initial height is ##h_{0} = 0##, or final height is ##0##, or final velocity is ##0##, or [...].

Let's say I am dealing with some task, I need to calculate ##v_{h}## (velocity at some height). After calculations I came up with this formula:

##v_{h} = \sqrt{v_{i}^2 - 2gh + 2gh_{i}}##, however the formula: ##v_{h} = \sqrt{v_{i}^2 - 2gh}## will work just as fine as the first one, because in the task it is said that initial height ##h_{i} = 0##.

1. Which approach, as a general advice, should be better? The first-formula one, which is a little bit more complex, however it'll work for more cases; or the second-formula approach, making it as simple as possible, directly addressing only the task-specific requirements. And not making the formula more general. What is better to score highest points as a general advice?

Perhaps you could imagine such energy-conversion scenario in some task:

##mgh_{i} + \frac{mv_{i}^2}{2} = mgh_{f} + \frac{mv_{f}^2}{2}##

Knowing from the task description that ##v_{f} = 0 \quad \land \quad h_{i} = 0## I can reduce the equation down to:

##\frac{mv_{i}^2}{2} = mgh_{f}##

and thus make it far simpler, but less general. Should I do it or not?

2. How important is sketching the situation (making the drawing) that describes the task? Like draw some falling ball, add some vectors to it etc etc. I indeed do understand that making the drawing is always a good idea and it helps to understand the task. But if I regardless did solve the task correctly, without doing any drawing, would you personally cut me off some grading points because of not making the drawing? How important is it grading-wise, basically?

Sometimes I find myself in a situation where I get the calculations right, the final answer is right, but the drawing might not be the finest representation of task's situation. Hence I feel like it's "risky" for me to make the drawing when I am unsure if my drawing is correct. I feel like I am better off not making the drawing when I am not 100% certain the drawing is correct.

3. Lastly, let's say the task is related to momentum of inertia of a disk. The formula ##I = \frac{1}{2}mR^2## is well known. Do you personally think if I derive this formula (nobody is asking me to do so), I could perhaps get some additional small-tiny-bit of points? ((moment of inertia is just an example))

Thanks for answersing those odd questions and helping me.

edit: thanks for moving my post to appropriate sub-forum :)

I don't have a chance to directly ask my teacher following questions, so I figured who else could know better but you guys. :)

I am dealing with fairly simple tasks. (you can view my post history to get the idea)

Often, in the task's description, the initial velocity is ##v_{i} = 0##, or initial height is ##h_{0} = 0##, or final height is ##0##, or final velocity is ##0##, or [...].

Let's say I am dealing with some task, I need to calculate ##v_{h}## (velocity at some height). After calculations I came up with this formula:

##v_{h} = \sqrt{v_{i}^2 - 2gh + 2gh_{i}}##, however the formula: ##v_{h} = \sqrt{v_{i}^2 - 2gh}## will work just as fine as the first one, because in the task it is said that initial height ##h_{i} = 0##.

**My questions:**1. Which approach, as a general advice, should be better? The first-formula one, which is a little bit more complex, however it'll work for more cases; or the second-formula approach, making it as simple as possible, directly addressing only the task-specific requirements. And not making the formula more general. What is better to score highest points as a general advice?

Perhaps you could imagine such energy-conversion scenario in some task:

##mgh_{i} + \frac{mv_{i}^2}{2} = mgh_{f} + \frac{mv_{f}^2}{2}##

Knowing from the task description that ##v_{f} = 0 \quad \land \quad h_{i} = 0## I can reduce the equation down to:

##\frac{mv_{i}^2}{2} = mgh_{f}##

and thus make it far simpler, but less general. Should I do it or not?

2. How important is sketching the situation (making the drawing) that describes the task? Like draw some falling ball, add some vectors to it etc etc. I indeed do understand that making the drawing is always a good idea and it helps to understand the task. But if I regardless did solve the task correctly, without doing any drawing, would you personally cut me off some grading points because of not making the drawing? How important is it grading-wise, basically?

Sometimes I find myself in a situation where I get the calculations right, the final answer is right, but the drawing might not be the finest representation of task's situation. Hence I feel like it's "risky" for me to make the drawing when I am unsure if my drawing is correct. I feel like I am better off not making the drawing when I am not 100% certain the drawing is correct.

3. Lastly, let's say the task is related to momentum of inertia of a disk. The formula ##I = \frac{1}{2}mR^2## is well known. Do you personally think if I derive this formula (nobody is asking me to do so), I could perhaps get some additional small-tiny-bit of points? ((moment of inertia is just an example))

Thanks for answersing those odd questions and helping me.

edit: thanks for moving my post to appropriate sub-forum :)

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