In this question use g=9.8 m s−2g = 9.8 \text{ m s}^{-2}g=9.8 m s−2.
A high-pressure water nozzle at a fountain is designed to eject water droplets upwards with an initial speed of 12.6 m s−112.6 \text{ m s}^{-1}12.6 m s−1.
The manufacturer's manual states that these droplets can reach a peak altitude of 8.18.18.1 metres above the nozzle exit.
Suppose that the nozzle is directed vertically upwards.
(i) Verify the claim in the manufacturer's manual.
(ii) State two modelling assumptions you have made in verifying this claim.
During operation, wind or mechanical drift may cause the nozzle to tilt from the vertical by an angle of up to 20∘20^{\circ}20∘.
The possible range of maximum heights, HHH metres, above the nozzle which can be reached by the droplets is expressed as C≤H≤8.1C \le H \le 8.1C≤H≤8.1
Determine the value of CCC, giving your answer to two significant figures.