8 A football is placed on a horizontal surface. It is then kicked, so that it has an initial velocity of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(40 ^ { \circ }\) above the horizontal.
- State two modelling assumptions that it would be appropriate to make when considering the motion of the football.
- Find the time that it takes for the ball to reach its maximum height.
- Hence show that the maximum height of the ball is 3.04 metres, correct to three significant figures.
- After the ball has reached its maximum height, it hits the bar of a goal at a height of 2.44 metres. Find the horizontal distance of the goal from the point where the ball was kicked.