Projectile Motion with air resistance (1 Viewer)

[vds700]

There was a question in the 2003 HSC on this, ad it spun me out a bit.

(b) A particle of mass m is thrown from the top, O, of a very tall building with an
initial velocity u at an angle α to the horizontal. The particle experiences the
effect of gravity, and a resistance proportional to its velocity in both the
horizontal and vertical directions. The equations of motion in the horizontal and
vertical directions are given respectively by

x: = −kx. and y: = −ky. − g x. is x dot and x: is x double dot

where k is a constant and the acceleration due to gravity is g. (You are NOT
required to show these.)
(i) Derive the result
x. = ue^(-kt)cosα
from the relevant equation of motion.
(ii) Verify that
y. = (1/k)[(kusinα + g)e^-kt - g]

satisfies the appropriate equation
of motion and initial condition.
(iii) Find the value of t when the particle reaches its maximum height.
(iv) What is the limiting value of the horizontal displacement of the particle?

Are we expected to be able to integrate these sorts of equations? I ask because I remember seeing in a thread a while ago that they took non-uniform circular motion out of the syllabus a couple of years ago, and just wondering whether it is the same with this. If it is examinable, could someone please tell me where I could locate some similar questions to practise on? I have a feeling it could come up (there hasnt been a projectile Q since 2003)

BTW I have the solutions book, ao i know how to do the question.

 

[u-borat]

i thought that resistance type questions were only in vertical motion...

 

[friction]

Wat question was it in the HSC i would love this question. If it was one of the back end questions.

 

[ronnknee]

If you think about it, projectile motion with resistance is about resolving the trajectory into the two components. From there you just integrate them like you would normally. It's nothing new

 

[ronnknee]

Wat question was it in the HSC i would love this question. If it was one of the back end questions.

2003 question 5

I did this like two days ago and I even had a visit on "2003 Exam Thoughts" forum just to check out what they thought. Heaps of them thought they failed the exam haha

 

[vds700]

If you think about it, projectile motion with resistance is about resolving the trajectory into the two components. From there you just integrate them like you would normally. It's nothing new

yeah, your right, it was just the format that threw me. If u make it

a = -kv
dv/dt=-kv
dt/dv=(-1/kv) then its pretty easy to integrate.

 

[friction]

Hard for a question 5 however.

 

[cccclaire]

oh man, part (ii) took me forever when I did it.

Got it out eventually though, it's actually not that difficult once you figure out what to do (and don't make really stupid mistakes like I did).

 

[ronnknee]

Part 2 requires product rule, I kinda got tricked because I had forgetten that v could be differentiated

 

[Trebla]

This is a "Harder 3 Unit" question meshed with Mechanics. You are expected to know how to apply the same principles of Mechanics (i.e. vectors diagrams and solving simple differential equations) in questions you've never seen before (Component B of the syllabus). This means that you can be asked ANYTHING which can be solved using the current mathematical tools you have.