m2 impulse exam question (edexcel)

I am really confused with q5 on this paper, I've tried approaching the question with vectors and for part a worked out:

mom before: 0.25(30i) = 7.5i
mom after: 0.25v

but not sure how to get an answer from there, and am clueless with part b

would appreciate some advice on how to tackle this thanks


Question paper: https://ca99c64778b62ba7e7b339967029e090c5733c3a.googledrive.com/host/0B1ZiqBksUHNYOXdJSDFGUUZPRUE/June%202012%20QP%20-%20M2%20Edexcel.pdf

mark scheme: https://ca99c64778b62ba7e7b339967029e090c5733c3a.googledrive.com/host/0B1ZiqBksUHNYOXdJSDFGUUZPRUE/June%202012%20MS%20-%20M2%20Edexcel.pdf

Read this and was wondering why you were saying mum before and mum after.

Anyways, vectors is slightly awkward here, let's resolve instead (which is almost the same thing as vectors)

If we consider only horizontal motion, we get:

Impulse = change in momentum. The horizontal component of impulse is $12.5 sin \alpha$ pointing to the left.

The speed of B horizontally is (let's say v):

The $12.5\sin \alpha = 0.25v - 0.25(-30)$ where we use - since the ball is moving 30 metres per second opposite to the impulse and we gave impulse a +12.5 sinalpha.

Anyways, since $\sin \alpha = 0.6$ we have: $12.5(0.6) = 0.25v + 7.5 \iff 7.5 = 0.25v + 7.5$, this gives $v=0$.

So there is no horizontal component of B, thank god, that makes life simple!

Now - let's consider vertical motion:

This gives us: $12.5\cos \alpha$ (impulse acts upwards)

And the change in momentum is $0.25u - 0$ (u is our vertical speed) and there is no vertical motion previous to the impulse.

So $12.5\cos \alpha = 0.25u \iff u = 4\times 12.5 \times 0.8 = 40$. So the speed is 40 vertical and 0 horizontal, and hence 40 overall.

And from this, since the 40 overall is acting vertically upwards, then the direction of travel of B is "perpendicular to the original direction". i.e: it went from pure horizontal to pure vertical.

thanksss so much, your explanation was really helpful, i understand it all now! can you be my personal maths tutor please

how come you are always so quick to reply to my problems hehe

thanksss so much, your explanation was really helpful, i understand it all now! can you be my personal maths tutor please

how come you are always so quick to reply to my problems hehe