Question

dimensional analysis test
directions: convert all of the following using your prior knowledge and the conversions below. you must show all work for full credit!!!
conversions:
1 hour = 60 min 1 mile = 5280 feet 1 yard = 3 feet 1 meter = 3.28 feet
1 km = 0.62 miles 1 kg = 2.2 lbs 1 inch = 2.54 cm 1 quart = 0.946 liters
1 foot = 12 inches 1 inch = 25.4 mm 1 mile = 1600 meters 1 gallon = 3.784 liter

1. 205 lbs into kilograms
2. 33689 seconds into years
3. 350 liters into gallons
4. 75 miles per hour into meters per second
5. 75 meters per second into miles per hour

Explanation:

Step1: Verify 205 lbs to kg

$\frac{205\ \text{lbs}}{1} \times \frac{1\ \text{kg}}{2.2\ \text{lbs}} = \frac{205}{2.2}\ \text{kg} \approx 93.18\ \text{kg}$

Step2: Convert 33689 sec to years

$\frac{33689\ \text{sec}}{1} \times \frac{1\ \text{min}}{60\ \text{sec}} \times \frac{1\ \text{hr}}{60\ \text{min}} \times \frac{1\ \text{day}}{24\ \text{hr}} \times \frac{1\ \text{year}}{365\ \text{days}}$
$= \frac{33689}{60 \times 60 \times 24 \times 365}\ \text{year} \approx 0.00107\ \text{year}$

Step3: Convert 350 liters to gallons

$\frac{350\ \text{liters}}{1} \times \frac{1\ \text{gallon}}{3.784\ \text{liters}} = \frac{350}{3.784}\ \text{gallons} \approx 92.49\ \text{gallons}$

Step4: Convert 75 mph to m/s

$\frac{75\ \text{miles}}{1\ \text{hr}} \times \frac{1600\ \text{meters}}{1\ \text{mile}} \times \frac{1\ \text{hr}}{60\ \text{min}} \times \frac{1\ \text{min}}{60\ \text{sec}}$
$= \frac{75 \times 1600}{60 \times 60}\ \text{m/s} \approx 33.33\ \text{m/s}$

Step5: Convert 75 m/s to mph

$\frac{75\ \text{meters}}{1\ \text{sec}} \times \frac{1\ \text{mile}}{1600\ \text{meters}} \times \frac{60\ \text{sec}}{1\ \text{min}} \times \frac{60\ \text{min}}{1\ \text{hr}}$
$= \frac{75 \times 60 \times 60}{1600}\ \text{mph} = 168.75\ \text{mph}$

Answer:

1. $\approx 93.18\ \text{kg}$
2. $\approx 0.00107\ \text{year}$
3. $\approx 92.49\ \text{gallons}$
4. $\approx 33.33\ \text{m/s}$
5. $168.75\ \text{mph}$