can anyone explain part b)?
The answers are there but I don't understand where all the fractions are coming from.
And why is both moving to left? Wouldn't that make this inelastic collision?
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If both move together after the collision, it doesn't mean that the collision is elastic. An elastic collision just means that the body is able to regain its original shape completely after collision.
If the second mass(pendulum) were not attached to the string, it would have not moved together with the other mass. But since it is attached to the string, it is compelled to move forward, and so is the other mass. They move together only for an instant, because just after that, the mass attached to the pendulum moves up, while the other mass moves forward linearly.
The second equation is just conservation of linear momentum. Clear now?