A rescue probe is launched straight up from the bottom of a narrow pit that is 5m deep. After leaving the pit mouth (ground level) it continues upward and finally comes to rest momentarily at a point 45m above the ground before descending back into the pit. Neglect air resistance and take g=9.8m/s2.
(i) Determine the initial speed with which the probe emerges from the pit mouth (ground level).
(ii) Calculate the time taken for the probe to rise from ground level to the highest point.
(iii) Find the speed of the probe just before it re-enters the pit at ground level on its way down.
(iv) Compute the total time elapsed from the instant the probe leaves the pit mouth to the moment it reaches the bottom of the pit again.