M4-elastic collisions... little help?

stuck on a couple of questions but its the method im not seeing so could someone give me a hand and work through this one with me:
Ex 2A
q8)

Two smooth vertical walls stand on a smooth horizontal floor, and intersect at an acute angle θ. A smooth small particle is projected along the floor at right angles to one of the walls and away from it. After one impact with each wall the particleis moving parallel to the first wall it struck. Given that the coefficient of restitution between the particles and each wall is e show that:
(1+2e)tan²θ=e²

thanks for any help, just cant see the answer...

Reply 1

KAISER_MOLE

Hey, how's the STEP going, ready for it? Just typing up the solution now.

Reply 2

arran

STEP is going... interestingly, im getting better at it tho, slowly. Whether ill be ready in time is to be seen, but as i have 6 4hour long STEP lessons this study leave, i hope so.

Reply 3

KAISER_MOLE

call theta = t for ease.

Now, the particle attacks the first wall with speed u, usint parellel, ucost perpendicular. So after first collision, travelling usint parellel to first wall, eucost perpendicular to first wall.

Now, to second wall, Parellel to the wall (and sort of up it) are the components

(usint)cost + (eucost)sint

Perpendicular and into it

(eucost)cost - (usint)sint

So after the second collision, it moves with u(e+1)sintcost parellel to second wall and up it, and eu(ecos²t - sin²t) and away from it. For this to be parellel to first wall, the vertical components of each must cancel out, i.e.

u(e+1)costsint . sint = eucost(ecos²t - sin²t)

=>

(e+1)sin²t = e²cos²t - esin²t

=> (2e+1)tan²t = e².

Q.E.D

Reply 4

KAISER_MOLE

Wow, 24 hours of it, cool :p:

- I'm doing my last mock on Friday and might get some help from a random Dude on the harder mechanics questions. Other than that, have to actually try help someone with AEA mathematics, which I know nout about!

Reply 5

JeremyC

How is STEP going for you then KAISER? I also have to do it. :wink:

The later (2000+) STEP III papers seem OK, but the earlier ones are somewhat tricky, due no doubt to the different syllabi. I did the 1998 STEP III this morning and probably got somewhere near the 2-1 boundary (hopefully just over - I need a 1 in both).

STEP II on the other hand appears to be relatively 'easy' compared to STEP III, so I'm only really concerned with STEP III.

As for AEA Maths - it's a farce compared to STEP. I did a few past AEA Maths papers at the beginning of the Easter holiday and was suprised by its relative ease. The questions are rather like hard A level questions, with little thought required compared to STEP questions - moments of "How the **** am I meant to do that?" which are rather common with STEP (I find) are rare.

Reply 6

KAISER_MOLE

Yeah, didn't like the 1998 STEP III, thought the 1999 one was gorgeous though. I need a 1,2 so perhaps a bit nicer (which college you get an offer from? ) .

Reply 7

JeremyC

Sidney. Their normal offer is 1,2 I think, but they gave out an abnormally high number of offers this year so they must have had to make the offer harder.

Which college did you apply to? St John's seems to ring a bell for some reason...

Reply 8

KAISER_MOLE

Correcto Mundo

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