Question

factor label method

example: it takes 0.173 days for light to travel from the sun to the closest planet in our solar system, mercury. how many seconds does it take?

1. write down the ku (known unit) measurement your calculated answer will depend on: 0.173 days

1. write down the conversion factors needed to take your given measurement and get to your end answer:

days → hours → minutes → seconds
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

1. write out your factor label method calculations and circle your final answer. write down all steps:

( 0.173 \text{ days} \times left( \frac{24 \text{ hr}}{1 \text{ day}}
ight) \times left( \frac{60 \text{ min}}{1 \text{ hr}}
ight) \times left( \frac{60 \text{ sec}}{1 \text{ min}}
ight) = )
( 0.173 \text{ days} \times left( \frac{24 \text{ hr}}{1 \text{ day}}
ight) \times left( \frac{60 \text{ min}}{1 \text{ hr}}
ight) \times left( \frac{60 \text{ sec}}{1 \text{ min}}
ight) = 14900 \text{ seconds} ) (rounded to 3 sig figs because 0.173 days has 3 sig figs)

1. the distance between trappist-1 solar system (a system with 7 earth-like planets) and earth is 39.0 light years. how many calendar years would it take for nasa’s space shuttle to get there at 17,500 miles per hour?

1. the external tank for the space shuttle carried 143,000 gallons of liquid oxygen. a gallon of liquid oxygen weighs 4.322 kg. nasa paid $2.6 per kg for liquid oxygen. how much did nasa spend in total on liquid oxygen for the external space shuttle tank, for one mission?

(c) bethany lau

Explanation:

Problem 2: Time to Travel to Trappist - 1

Step 1: Recall the speed of light and convert light - years to miles

The speed of light \(c = 186000\) miles per second. One light - year is the distance light travels in one year.
First, find the number of seconds in a year:

• Number of hours in a year: \(365\) days/year\(\times24\) hours/day \( = 8760\) hours/year
• Number of minutes in a year: \(8760\) hours/year\(\times60\) minutes/hour \(= 525600\) minutes/year
• Number of seconds in a year: \(525600\) minutes/year\(\times60\) seconds/minute \( = 31536000\) seconds/year

The distance of one light - year \(d_{ly}=186000\) miles/second\(\times31536000\) seconds/year\(=5.865696\times 10^{12}\) miles/year

The distance to Trappist - 1 is \(d = 39.0\) light - years. So the total distance \(D=39.0\times5.865696\times 10^{12}\) miles \(=2.28762144\times 10^{14}\) miles

Step 2: Use the formula \(t=\frac{D}{v}\) to find the time in hours

The speed of the space shuttle \(v = 17500\) miles per hour.
\(t=\frac{2.28762144\times 10^{14}\text{ miles}}{17500\text{ miles/hour}}\)
\(t=\frac{2.28762144\times 10^{14}}{1.75\times 10^{4}}\) hours \(=1.307212251\times 10^{10}\) hours

Step 3: Convert hours to years

Number of hours in a year \(h_{year}=8760\) hours/year
\(t_{years}=\frac{1.307212251\times 10^{10}\text{ hours}}{8760\text{ hours/year}}\)
\(t_{years}\approx1.49225\times 10^{6}\) years

Problem 3: Cost of Liquid Oxygen for Space Shuttle

Step 1: Find the total mass of liquid oxygen

The volume of liquid oxygen \(V = 143000\) gallons.
The mass per gallon \(m_{gallon}=4.322\) kg/gallon.
The total mass \(M=143000\) gallons\(\times4.322\) kg/gallon
\(M = 143000\times4.322=618046\) kg

Step 2: Calculate the total cost

The cost per kg \(C_{kg}=\$2.6\) per kg.
The total cost \(TC = M\times C_{kg}\)
\(TC=618046\) kg\(\times\$2.6\) per kg
\(TC=\$1606919.6\)

Problem 2 Answer:

\(\approx1.49\times 10^{6}\) years (rounded to 3 significant figures)

Problem 3 Answer:

\(\$1606920\) (rounded to the nearest dollar)

Answer:

Step 1: Find the total mass of liquid oxygen

The volume of liquid oxygen \(V = 143000\) gallons.
The mass per gallon \(m_{gallon}=4.322\) kg/gallon.
The total mass \(M=143000\) gallons\(\times4.322\) kg/gallon
\(M = 143000\times4.322=618046\) kg

Step 2: Calculate the total cost

The cost per kg \(C_{kg}=\$2.6\) per kg.
The total cost \(TC = M\times C_{kg}\)
\(TC=618046\) kg\(\times\$2.6\) per kg
\(TC=\$1606919.6\)

Problem 2 Answer:

\(\approx1.49\times 10^{6}\) years (rounded to 3 significant figures)

Problem 3 Answer:

\(\$1606920\) (rounded to the nearest dollar)