In this question use g=9.8 m s−2g = 9.8 \text{ m s}^{-2}g=9.8 m s−2.
A decorative water fountain nozzle is designed to eject water droplets vertically upwards with an initial speed of 11.2 m s-1. The manufacturer’s catalog states that the water can reach a maximum vertical height of 6.4 metres above the nozzle.
(i) Verify the manufacturer's claim by calculating the maximum height of a droplet when fired vertically.
(ii) Identify two modelling assumptions used in this verification.
The nozzle's alignment can deviate by as much as 20∘20^{\circ}20∘ from the vertical.
The range of possible maximum vertical heights, h h\,h metres, reached by the droplets can be expressed as:
k≤h≤6.4 k \le h \le 6.4 k≤h≤6.4Calculate the value of kkk, giving your answer to two significant figures.