I think it's going to go something like
1) Show such a t exists.
2) Show t=1 (assume <1 and get a contradiction).
I suspect that connectedness and/or compactness will come into play, but I can't see the answer immediately.
I have a problem showing that any vector bundle is trivial.
The hint given with the exercise is considering the biggest number so that is trivial, but i don't get how to do that, in fact I'm not even sure what that last statement means.
So far I think I've shown that for some , we have a homeomorphism , since there must exist a homeomorphism to an open neighbourhood of 0, and we can restrict that. Also, is homeomorphic to . But where do I go from there?