$$A diver of mass $65$ kg takes off from the $10$ m platform from a standing position by jumping upwards with a $($near$)$ vertical speed of $2\mathrm{.}0$ ms$-1.$ 

a$)$ Calculate

i$)$ the time taken to reach the water;

ii$)$ the initial gravitational potential energy;

iii$)$ the initial kinetic energy.

b$)$ Use $2$ methods $($uniform motion equations and the principle of conservation of energy$)$ to check the accuracy of the statement at the beginning of the passage that a diver jumping from the high platform will hit the water at $30$ mph$.$ 

c$)$ Sketch graphs of i$)$ displacement against time and ii$)$ velocity against time for the dive, pointing out the important features of the graphs and the relationship between the two graphs.