A variable rate granular fertilizer applicator receives a prescription to apply $120\text{ kg/ha}$ of urea. The working swath width is $12\text{ m}$ and the travel speed is $7.2\text{ km/h}$ ($2.0\text{ m/s}$). Calculate the required total mass discharge rate of the applicator in $\text{kg/s}$ (round off to 3 decimal places).
Answer Key:
0.288
Step-by-Step Solution & Explanation
Forward speed $v = 2.0\text{ m/s}$.
Swath width $W = 12\text{ m}$.
Area coverage rate per second:
$a = W \times v = 12\text{ m} \times 2.0\text{ m/s} = 24.0\text{ m}^2/\text{s} = 0.0024\text{ ha/s}$
Application rate $R = 120\text{ kg/ha}$.
Total mass discharge rate:
$\dot{m} = R \times a = 120\text{ kg/ha} \times 0.0024\text{ ha/s} = 0.288\text{ kg/s}$