Discussion
A field sprayer with 12 nozzles fitted to the boom at a spacing of 0.5 m is used for spraying at a height of 0.75 m from the ground. The angle of spraying is 75°. If the height of spraying is reduced to 0.6 m, the change in swath in m is
Answer: A
The swath narrows by 0.23 m.
Each nozzle sprays a cone of included angle 75 degrees, so its swath width at height h is \(2h\tan 37.5^{\circ}\). The boom's overall swath is the nozzle spacing times the gaps between nozzles plus the spread of the end nozzles, and only that spread depends on the height:
\[ \begin{aligned} \Delta W &= 2\,\Delta h\, \tan 37.5^{\circ} \\ &= 2 \times (0.75 - 0.60) \times 0.767 \\ &= 0.23\ \text{m} \end{aligned} \]
Counting the change once per nozzle instead of once for the boom multiplies it by 12, which is not offered, and using tan 75 degrees in place of the half-angle gives 1.12 m. 0.48, 0.65 and 0.91 are not produced by this geometry.
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