Question

If your front lawn is 15.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1150 new snow flakes every minute, how much snow (in kilograms) accumulates on your lawn per hour? Assume an average snow flake has a mass of 2.20 mg.

Answer 1

To calculate the amount of snow that accumulates on the lawn per hour, multiply the area of the lawn by the number of snowflakes that accumulate per hour. Then, multiply the number of snowflakes by the mass per snowflake to find the mass of the snow that accumulates. Finally, convert the mass from grams to kilograms.

Step-by-step explanation:

To calculate the amount of snow that accumulates on your lawn per hour, we first need to find the area of your lawn. The area is the product of the width and length, which is 15.0 feet x 20.0 feet = 300.0 square feet.

Next, we calculate the total number of snowflakes per hour. Since each square foot accumulates 1150 snowflakes per minute, we can multiply this value by 60 to get the snowflakes per hour. So, 1150 snowflakes/minute x 60 minutes/hour = 69,000 snowflakes/hour.

Finally, we can find the mass of the snow that accumulates by multiplying the number of snowflakes by the mass per snowflake. So, 69,000 snowflakes/hour x 2.20 mg/snowflake = <<69000*2.20=151800>>151,800 mg/hour. To convert this mass to kilograms, we divide by 1,000: 151,800 mg/hour ÷ 1,000 = 151.8 grams/hour = 0.1518 kilograms/hour.

Answer 2

First, we calculate the total are:
Area = 15 x 20
Area = 300 sq ft

Snowflakes accumulated per minute = 1150 x 300
Snowflakes per minute = 345,000 snowflakes per minute

Snowflakes per hour = 345,000 x 60
Snowflakes per hour = 20,700,000
Snowflakes per hour = 20.7 x 10⁶

Mass of one snowflake = 2.2 mg
Mass of one snowflake = 2.2 x 10⁻³ g
Mass of one snowflake = 2.2 x 10⁻⁶ kg

Mass of snow = 20.7 x 10⁶ x 2.2 x 10⁻⁶
Mass of snow = 45.54 kg per hour