For anyone who actually did fm1, here's what I did.
The 9 mark impulse Q gave the impulse in terms of lambda and mu, the initial velocity, and said it was deflected by 45 degrees. Find the possible values of lambda and mu.
I wrote the final velocity in terms of lambda and mu. Then, I put this into the dot product formula with initial velocity as given, and angle=45.
Then you get an expression with lambda and mu in it and you can rearrange etc etc, going through a lot of unpleasant algebra, and get to the answer that way