8. A golf ball is hit with initial velocity \(u \mathrm {~ms} ^ { - 1 }\) at an angle of \(45 ^ { \circ }\) above the horizontal. The ball passes over a building which is 15 m tall at a distance of 30 m horizontally from the point where the ball was hit.

1. Find the smallest possible value of \(u\). When \(u\) has this minimum value,
2. show that the ball does not rise higher than the top of the building.
3. Deduce the total horizontal distance travelled by the ball before it hits the ground.
4. Briefly describe two modelling assumptions that you have made.