Projectile motion- equations or intergration (1 Viewer)

[mcsmells]

Hey dudes
Hows it going
Well
I was just wondering which method other people use and find the easiest when doing stuff with projectile motion.
I mean like do you prefer to intergrate the acceleration and velocity to get the answer, or do you prefer to use those equations to find answer.
I was only wondering this because i got one of my pals who does four-unit to help me with a question, and i had started off with the equation s=ut+1/2at^2. And then he like psyched up, well not really psyched up but was like "You idiot! never use the equations always intergrate them. And so he then showed me how to do it. Like intergrate the horizontal and vertical acceleration, and then get the velocity, and intergrate it, then get the horizontal and vertical displacement, etc...
OK well
I now use this method and so far i am finding it actually easier intergrate the stuff rather than remembering the equations. I was just wondering whether this method was always a better one, and what method other people use.
Love pieter

 

[king_of_boredom]

funny you mention that, i just had a 3 unit assessment and i did very well in projectile motion - that's becuase i use the method your 4 unit friend does, that is, integrate the vertical and horizontal acceleration. personally, i find them easier to use, it saves a lot of time in exams, and most people in my class use them as well. i actually recommend that you memorise all formulas, ie. max height, range, max range, cartesian eq., time of flight, etc. but whichever method you use is up to you.

 

[acmilan]

Unless you are given the equations in the question, you must always integrate them starting with x'' = 0 and y'' = - g (if you take upwards as positive, which is the convention). More often then not marks are awarded for intermediate steps, and simply learning the formula and plugging in numbers will only get you the marks they assign for the final answer. Not to mention if you get the final answer wrong, atleast showing them how you got to the formula will entitle you to some marks.

 

[FinalFantasy]

formulas like
s=ut+1\2 at²
v=u+at
v²=u²+2as
are not to be used in mathematics in HSC, they only work when acceleration is constant, and don't work in lots of the q's in 3unit. and even when it does work, u can't use them, dey expect u to integrate to get ur equations

 

[king_of_boredom]

Unless you are given the equations in the question, you must always integrate them starting with x'' = 0 and y'' = - g (if you take upwards as positive, which is the convention). More often then not marks are awarded for intermediate steps, and simply learning the formula and plugging in numbers will only get you the marks they assign for the final answer. Not to mention if you get the final answer wrong, atleast showing them how you got to the formula will entitle you to some marks.

so in the HSC examination, if we want to use those formulas, we have to derive them? will we lose marks for just using formulas and putting the numbers in? i mean, i know the steps on how to integrate them, but doesn't that just waste time?

 

[acmilan]

so in the HSC examination, if we want to use those formulas, we have to derive them? will we lose marks for just using formulas and putting the numbers in? i mean, i know the steps on how to integrate them, but doesn't that just waste time?

If they give you the equations to use then you dont have to derive them. Otherwise it is highly likely that some marks in the marking guidelines are given to deriving the equations. If you dont derive, you dont get those marks. Often the question actually asks you to derive the formula for range, max height etc. If you memorise them then you'll get 0 for questions like that. You have to remember that projectile motion in extension 1, unlike in physics, often requires you to work with algebra rather than actually subbing in numbers. Memorising the equations wont help in these cases

 

[KFunk]

If you really wanted to use them and you had a graph where the motion had uniform acceleration then they aren't too hard to derrive.

If you've got initial velocity u and a later velocity v ( where v > u ---> or v < u ) then you can use the fact that the area under a velocity vs. time curve is the distance travelled. You just sum together the rectangle and the triangle (using the case ( v > u ):

s = ut + 1/2(v - u)t
s=ut+1\2 at² (1)

Using the equation v=u+at (2) that was used to get (1) in the first place, [also note that (1) can be differentiated to obtain (2) ] you can sub it in once more to get rid of the t terms to produce:

v²=u²+2as (3)

While they're nice simple formulae to deal with, it'd probably save more time to do your normal mechanics/apps integration/differentiation processes.