2006 HSC MX2 Q6b(iv)(2)

[frog0101]

What is the correct solution to this question, there are several solutions on the internet and in HSC textbooks. Terry Lee solutions says  that the answer is (uR)/(gR-u^2) (https://thsconline.github.io/s/yr12/Maths/hscpapers_extension2.html) and then my MX2 2005-2014 book by MANSW says that is a different answer (2uR)/(gR-u^2).

Any help would be fantastic, and if the method to the correct solution could also be given

[RuiAce]

I don't agree with Terry Lee's answer. It would appear as though he subbed \( \boxed{x=D} \) into the equation given in iii). The correct choice is to substitute in \( \boxed{x=R} \), as we want to find the time taken to reach the surface of the planet, not what's essentially the maximum height.

MANSW is correct.