Question

If your front lawn is 16.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1350 new snowflakes every minute, how much snow, in kilograms, accumulates on your lawn per hour? Assume an average snowflake has a mass of 1.50 mg.

Answer 1

1) List known values.

Width: 16.0 ft

Length: 20 ft

Rate of accumulation: 1350 snowflakes/(ft2 * min)

2) List unknown values

Accumulated snow per hour:

3) Accumulated snow (grams) in one square foot of lawn per minute

`\text{Acc}_(snow)=1350(snowflakes)/(ft^2\cdot\min)\cdot\frac{1.50mg}{1\text{ snowflake}}\cdot\frac{1\text{ g}}{1000mg}=2.025(g)/(ft^2\cdot\min )`

2.025 g is the snow accumulated in one square foot in one minute.

4) Accumulated snow in one square foot per hour

`2.025(g)/(ft^2\cdot\min)\cdot(60\min)/(1h)=121.5(g)/(ft^2\cdot h)`

121.5 g is the snow accumulated in one square foot in one hour.

5) Calculate the area of the lawn

16.0 ft * 20.0 ft = 320 ft2

6) Accumulated snow on the whole lawn in one hour.

`121.5(g)/(ft^2\cdot h)\cdot(320ft^2)/(1)=38880(g)/(h)`

38880 g is the snow accumulated in one hour on the lawn.

7) Convert grams into kilograms

38.88kg is the amount of snow accumulated on the lawn in one hour.