Urgent collisions 2 dimensions ! I have Alevels pls help

Question is below

To make it look better

Could I have left it as - 3i and 4 j

No because that’s not a unit vector.

You can leave it as -3/5 i + 4/5 j tho if that’s what you’re

How did we know by pulling out a fifth we would get a unit vector

Just divide by the magnitude of a vector to make it unit ... the magnitude here is obvious since it is related to the 3,4,5 triangle.

I understand you thnaks ! I just don’t get why it has to be a unit vector

R they using a Paticular formula for part b ?!
Cause I dotn see how they are getting the answer

You need to use the dot product here to project the before/after velocities onto the unit impulse vector.

In other words, you are finding the before/after speeds of the ball perpendicular to the wall before writing down a relationship between them using the coeff of restitution.

-eu.I=v.I
In the Dr Frost mechanics slides.
u= initial velocity
v= final velocity