Question

if your front lawn is 25.0 ft wide and 20.0 ft long, and each square foot of lawn accumulates 1450 new snowflakes every minute, how much snow (in kilograms) falls on your lawn per hour? assume an average snowflake has a mass of 1.80 mg. strategy: first, calculate the rate at which snowflakes fall on one square foot (flakes per square foot per hour): \\(\left(\frac{1450 \text{ flakes}}{\text{min} \cdot \text{ft}^2}\
ight)\left(\frac{60 \text{ min}}{1 \text{ h}}\
ight) = 8.70 \times 10^4 \frac{\text{flakes}}{\text{h} \cdot \text{ft}^2}\\) next, determine the rate at which snowflakes fall on the entire lawn (per hour).

Explanation:

Step1: Calculate lawn area

$\text{Area} = 25.0\ \text{ft} \times 20.0\ \text{ft} = 500.0\ \text{ft}^2$

Step2: Total snowflakes per hour

$\text{Total flakes} = 8.70 \times 10^4\ \frac{\text{flakes}}{\text{h·ft}^2} \times 500.0\ \text{ft}^2 = 4.35 \times 10^7\ \frac{\text{flakes}}{\text{h}}$

Step3: Convert mass to kilograms

First, total mass in mg: $4.35 \times 10^7\ \text{flakes} \times 1.80\ \frac{\text{mg}}{\text{flake}} = 7.83 \times 10^7\ \text{mg}$
Then convert mg to kg: $7.83 \times 10^7\ \text{mg} \times \frac{1\ \text{kg}}{10^6\ \text{mg}} = 78.3\ \text{kg}$

Answer:

78.3 kilograms