Why Can't I Use Time Dilation to Calculate Relative Time for the Ball?

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I agree with a, b, and c1.

I'm not sure about c2, it might be correct. I would have used the relativistic velocity-addition formulas.

When I used to work out these kinds of problems, I would write down values of any gamma factors I calculate along the way. That saves time, not having to recalculate it when they often get used repeatedly. It's also an intermediate check, when I'd end up with a wrong answer and am tracking down where the mistake was.
 
Yea. Velocity transformation is another way of doing it. But the answer is different. Why I can't use time dilation to calculate the relative time taken for the ball to travel in this case?
 

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