FM1 question

I'm just getting confused because e<0<=1 and we're told that 0<lambda<1/2, and I don't know which one I'm supposed to use, if that makes sense?

can you post what you've tried?

I mean I've tried equating the answer from part a, but it just turned into a mess and I wasn't getting anywhere near the answer.
how would I start it?

Just do conservation of momentum equation and e x approach speed = separation speed

I got (a) from these.

oh I've got the answer to part a, I'm stuck on b?

I edited my post - I rearranged the expression for e to get k.

which restrictions do I use?
there are two? e<0<=1 and 0<lambda<1/2? Do I need to use both? If so which one should I start with?

which restrictions do I use?
there are two? e<0<=1 and 0<lambda<1/2? Do I need to use both? If so which one should I start with?

Well you want to find the minimum value of k, if that helps?

I used e as I said and got an inequality for k - it might not be the only approach

ok thanks, but if you had used the other inequality and got the correct answer, would you still get all the marks? x

which restrictions do I use?
there are two? e<0<=1 and 0<lambda<1/2? Do I need to use both? If so which one should I start with?

@mqb2766 ^ sorry for tagging you, please could you help😭 I just keep getting questions like these wrong ):

What do you get when you rearrange the inequality
e < 1
In terms of k?

Note, your original e < 0 < 1 isn't right as I'm sure you realize, it should be 0 < e < 1. The 0 < e is trivially satisfied (the numerator & denominator is positive) so just consider e < 1.

that gives 1<k(-2λ +1)


oh yeah sorry, that was a typo.
so in questions like this, we always ignore the 0<e?
because if I had re-arranged e>0, it gives that gives kλ>-1. Isn't that important information? idk

Thats (both) correct. For e > 0, k and lambda are both > 0, so
k*lambda > 0 > -1
So trivially satisfied, so not important for this question.

Note that when lambda=0, e=1 and k=1, this was essentially a Newton's cradle question where a moving ball collides with a stationary, identical ball and the first ball is brought to a complete halt and transfers all its velocity to the second ball. This is the scenario that gives the k=1 condition.

Thats (both) correct. For e > 0, k and lambda are both > 0, so
k*lambda > 0 > -1
So trivially satisfied, so not important for this question.

Note that when lambda=0, e=1 and k=1, this was essentially a Newton's cradle question where a moving ball collides with a stationary, identical ball and the first ball is brought to a complete halt and transfers all its velocity to the second ball. This is the scenario that gives the k=1 condition.

Also, what do I do after that bit? where do I use this 0<lambda<1/2 lol😭