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

[tanzl]

I am new to this topic. Please correct me if there is any mistakes.
http://i359.photobucket.com/albums/oo31/tanzl/JavaPrinting-4.jpg

 

[Redbelly98]

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.

 

[tanzl]

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?