A cyclist exerts a constant driving force of magnitude \(F\) N while moving up a straight hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac{36}{325}\). A constant resistance to motion of 32 N acts on the cyclist. The total weight of the cyclist and his bicycle is 780 N. The cyclist's acceleration is \(-0.2 \text{ m s}^{-2}\).

(i) Find the value of \(F\).

The cyclist’s speed is 7 m s^-1 at the bottom of the hill.

(ii) Find how far up the hill the cyclist travels before coming to rest.