Projectile Motion (2 Viewers)

[untamedanimal]

I havnt done the topic yet but is projectile motion in maths exactly like that of Physics. I basically have mastered the physics topic after a while and was wondering if the maths topic will be just as easy or harder

 

[Affinity]

harder

 

[CM_Tutor]

Definitely harder. Maths handles projectile motion properly by using calculus - unlike Physics - and also includes questions Physics would never dare ask, like firing up / down inclined planes, and at moving targets.

 

[Heinz]

Originally posted by untamedanimal
I havnt done the topic yet but is projectile motion in maths exactly like that of Physics. I basically have mastered the physics topic after a while and was wondering if the maths topic will be just as easy or harder

Theres not much to master in physics projectile motion anyway. 3unit projectiles are heaps more interesting and unlike physics you derive your formulas instead of being spoonfed

 

[Calculon]

Ohhh! This all sounds great, I can't wait for 4u mechanics

 

[Grey Council]

mate, i dunno about "i can't wait till 4u mechanics". Are you insane? wtf, i dunno how smart you are, but its pretty difficult to do the questions in the 3u cambridge.

And if you do the extension question in the cambridge book in the projectile motions chapter, i'll give you $10.

 

[Xayma]

Well if you really want I have a few mechanics questions from an engineering mechanics textbook, I havent compared them to the 4U mechanics but if you want some I can give you some.

 

[Heinz]

Originally posted by Xayma
Well if you really want I have a few mechanics questions from an engineering mechanics textbook, I havent compared them to the 4U mechanics but if you want some I can give you some.

A friend of mine said that the mechanics in engineering is pretty hard. He got 95 for 4unit last year i think (accelerated)

 

[Xayma]

Its not that they are hard, it is that they can be very hard and require a fair bit of thought.

I havent touched a fair few of those in that textbook because some first year engineering students also use it, so they can get hard.

 

[Grey Council]

so whoever is looking forward to 4u mechanics is either crazy or very good at maths (OR enjoys applications of calculus).

lol, thats all the possibilities. ^_^

 

[...]

*waits for Keypad's reply*

 

[Grey Council]

hokay, do this:
A large vertical wall stand on horizontal ground. The nozzle of a water hose is positioned at a point C on the ground at a distance c from the wall and the water jet can be pointed in any direction from C. Also the water issues from the nozzle with speed V . (Air resistance may be neglected and the constant g denotes the acceleration due to gravity.)
(i) Prove that the jet can reach the wall above ground level if and only if V >(gc)^1/2.
(ii) If V = 2.(gc)^1/2 prove that the portion of the wall that can be reached by the jet is
a parabolic segment of height (15c)/8 and area (5.sqrt15(c^2))/2.

 

[nike33]

(i) Prove that the jet can reach the wall above ground level if and only if V >(gc)1/2.
(ii) If V = 2.(gc)1/2 prove that the portion of the wall that can be reached by the jet is
a parabolic segment of height (15c)/8 and area (5.sqrt15(c^2))/2.


i))

i cant be bothered deriving formulas or watever...but maximum rangle v^2 = xg ..v = sqr(xg) taking it as positive

now let the base of the wall be the origon hence C(c,0)
now for the water to hit the wall at ground level exactly v = sqr(gc) as x = c

obviously now as v increases the distance increases. hence as
v = sqr(gc) hits the wall at ground level, if v > sqr(gc) it must hit the wall. and only if v > sqr(gc) as allready stated, this is the maximum range obtanible

 

[nike33]

ahh ii) took me lik 2 pages, ill scan and post it 2moorow

 

[Grey Council]

argh, your not in year 12, are you? :-\

and it wasn't meant to be for you. I posted up those questions for those people who thought that projectile motion is easy.
It isn't. It's pretty darn hard.

That's a 4u question 10, from 1974 ( i think ) maths paper, so maybe i shouldn't have posted it. ^__^
But then, its in the cambridge 3u book, in the extension section of projectile motion, so I think it isn't all TOO inappropriate.

 

[nike33]

"argh, your not in year 12, are you? :-\"

err yes

allright then if you dont want the answer for ii) ill give some hints for those wanting to try it. getting (15c)/8 shouldnt be that hard - just alot of algebra

then consider the height of the wall the y axis the 'jet' on the x axis and then the width of the wall on a new 'z' axis find the equation of the paraboa in terms of z and y (find the points where the parabola cuts the z axis and when z = 0 y = (15c)/8 then intergrate hence finding the area

 

[CM_Tutor]

Originally posted by nike33
then consider the height of the wall the y axis the 'jet' on the x axis and then the width of the wall on a new 'z' axis find the equation of the paraboa in terms of z and y (find the points where the parabola cuts the z axis and when z = 0 y = (15c)/8 then intergrate hence finding the area

Did you actually prove that the shape on the zy axis was a parabola? Or, did you note that when z = 0, y = 15c / 8, then find the two vakues of z when y = 0, and assume that the shape was parabolic before finding the area? - Incidentally, the area would be easiest found using Simpson's Rule.

 

[nike33]

i found when @ = 45 (ie max distance) then let the point p(x,y,z) be a point representing the water path.

i found that p(x,y,z) is equidistant from the line (0,31c/8,z) and the point (0, -c/8, 0) hence the pt P is a locus representing a parabola..etc

the reason i said find the co-ords of z = 0 was so when intergrating you know its between csqr(15) and -csqr(15) and can find area (thx for reminding me on simpsons rule btw! )

 

[~*HSC 4 life*~]

OH NOOOOOOOOO

i didn't choose physics for a reason!!!!!!!!!!!!!!!!!

 

[untamedanimal]

You didnt chose physics solely to avoid projectile motion?