question :s :S (1 Viewer)

[HSC :(]

hey this is from the 1978 paper...


yeh i know it sounds weird doin a paper from sucha long time ago... butman... theyre sooooo much harder then the recent papers, good practise


anyhoo..

heres the question

two cars represented by points a and b are travelling east and due north respectively along two roads represented by 2 straight lines intersecting at O. AT a certain instant car A is 2 km west of O and car B is 1 km south of O the former travelling at a constant speed of 1 km per minute and the latter the at constant speed V km per hour.


what value of v will cause a collision?

and then find in the course of motion the minimum distance b/w the cars

plz get bak to me as soon possible

thanx a bunch

 

[Affinity]

i) hmm it's takes ! 2 mins to reach O, so it should take B 2 mins to reach ) too.. so V = 0.5 km/min

ii) imagine a cartesian plane with origin at O.

now, A's position is (-2,0), B is at (0,-1) initially

their position at time t will be

A( (t-2), 0)

and

B( 0,(Vt - 1) )

so the square of the distance between them at time t is

D^2 = (t-2)^2 + (Vt - 1)^2

expanding

D^2 = (V^2 + 1)*t^2 - (2V + 4) t + 5

this is a quadratic with positive leading coefficient,
so it's minimum value will occur when
t = (-b/2a) = (2V + 4)/(V^2 + 1)

and we know this is positive.

substituting

D^2 = (V^2 + 1)*[(2V + 4)/(V^2 + 1)]^2 - (2V + 4)[(2V + 4)/(V^2 + 1)] + 5

D^2 = (2V + 4)^2 - (2V + 4)^2 / (v^2 + 1) + 5

and simplify etc.

 

[kimmeh]

would thattype of question still be in the syllabus?

 

[Affinity]

this is an easy question, just looks messy coz it's typed up here

 

[Bucko]

The 1978 paper is the hardest I've come across, and it's a lot easier these days.