Two asteroids

of equal mass collide as shown in the
figure. After the collision, asteroid A’s
trajectory is deflected by 30 degrees
from its initial motion. Asteroid B is
initially at rest and its final velocity
makes a 45 degree angle with respect
to the initial trajectory of asteroid A.

a) What is the final speed of each asteroid? Express your answer as a vector.

b) What fraction of asteroid A’s initial kinetic energy dissipates during the collision?

I still don't understand what you are trying to say.

The initial velocity before A hit B was 40 m/s

Vb = Va sin 30/sin 45

then
Via = Va cos 30 + (Va sin 30/sin 45)cos 45

so Via = 40

You did not say that
use it

so you can solve for Va, the speed of A after

then for Vb the speed of B after

what is Va? That is what is confusing me the most

Va is the speed of A after collision

how would i do part b?

once you have Va and Vb

Ke before = (1/2) m Via^2

Ke after = (1/2) m Va^2 + (1/2) m Vb^2

note m cancels everywhere in this problem

I think you can do the lost over the initial