8. A stone, of mass 1.5 kg , is projected horizontally with speed \(4 \mathrm {~ms} ^ { - 1 }\) from a height of 7 m above horizontal ground.

1. Show that the stone travels about 4.78 m horizontally before it hits the ground.
2. Find the height of the stone above the ground when it has travelled half of this horizontal distance.
3. Calculate the potential energy lost by the stone as it moves from its point of projection to the ground.
4. Showing your method clearly, use your answer to part (c) to find the speed with which the stone hits the ground.
5. State two modelling assumptions that you have made in answering this question.