Mechanics

B must be moving at a lower velocity than C after the collision.

Otherwise you'd have to invent the physics for B to pass through C.

I know that,but I don’t know how to find the answer, is the value of k that I stated above also part of the range of values that I could be since it means that B will be stationary thus no further collisions

If B has negative velocity it will collide with A, so that is one limit (B post impact velocity = 0). This will occur if k is large and and effectively B bounces off a wall (heavy C). If k is small (light C), both B and C will move in the same direction after the collision and the velocity of C will be larger than B, so I can't see a lower limit for k, apart form the obvious physcial k>0.

So essentially k=8 as I proved and bigger than 0.This doesn’t answer the question in the range of values k must be.

Ive not checked your working, but you want the post impact velocity of B to be >= 0, assuming the pre impact velocity of B is postive. That gives you a range for k, as described in the previous response

It would make sense to find the lower limit of k by using inequalities whereby
velocity B<=velocity A ,after impact since they could coalesce

I guess you need to understand (analyze the impact equation) why this is impossible, but the original reply is still valid.

I’m so confused.What is the answer to the it??

I don't know what your current answer is. You need to use the inequality in the velocity of B to get the inequality (upper limit) for k.

If you keep asking about a lower limit for k, you should do a thought experiment and understand why this won't occur.

My current answer is k=8
However I tried doing an inequality but it came out to be messy

Maybe try and make it less messy? If you're confident that k=8 corresponds to zero B velocity, it would be easy enough to argue that that would be the inequality boundary.

Could Veocity of C be the same as velocity of B

Doing thought experiments like these can be useful, but you should put the scenarios into the equation(s) and see what comes out.

Doing thought experiments like these can be useful, but you should put the scenarios into the equation(s) and see what comes out.

You can’t put this into equations since I’m setting the boundaries of the values of what k could be therefore I’ll have to decide if it’s possible

Can you post the full working, so the bits before you write v1 (and what does it refer to etc).