Dimensional Analysis Worksheet 2 | Summaries Dimensional Analysis ... - Free Printable

Since the user has set all options to false, I will proceed directly to solving the problems presented in the worksheet image. The image contains a "Dimensional Analysis Worksheet 2" with several conversion problems. I will solve each one step-by-step using dimensional analysis (unit conversion).

Problem 1: Convert 50 years into seconds.
* Given: 50 years
* Goal: Seconds
* Conversion Factors Needed:
* 1 year = 365 days
* 1 day = 24 hours
* 1 hour = 60 minutes
* 1 minute = 60 seconds
* Calculation:
$$50 \text{ years} \times \frac{365 \text{ days}}{1 \text{ year}} \times \frac{24 \text{ hours}}{1 \text{ day}} \times \frac{60 \text{ minutes}}{1 \text{ hour}} \times \frac{60 \text{ seconds}}{1 \text{ minute}}$$
$$= 50 \times 365 \times 24 \times 60 \times 60$$
$$= 1,576,800,000 \text{ seconds}$$
*(Note: The handwritten answer on the sheet says $1.58 \times 10^9$, which is the scientific notation for this number).*

Problem 2: How many weeks are in 2000 years?
* Given: 2000 years
* Goal: Weeks
* Conversion Factors Needed:
* 1 year = 52 weeks (approximate) OR use days: 1 year = 365 days, 1 week = 7 days. Let's use the more precise path.
* Calculation:
$$2000 \text{ years} \times \frac{365 \text{ days}}{1 \text{ year}} \times \frac{1 \text{ week}}{7 \text{ days}}$$
$$= \frac{2000 \times 365}{7}$$
$$= \frac{730,000}{7}$$
$$\approx 104,285.7 \text{ weeks}$$
*(Looking at the handwriting, it seems they might have used a simpler factor or rounded differently, but standard conversion yields approx 104,286 weeks).*

Problem 3: A car gets 25 miles per gallon. How many liters of gasoline does it need to travel 300 kilometers?
* Given: Distance = 300 km, Efficiency = 25 miles/gallon
* Goal: Liters of gas
* Conversion Factors Needed:
* 1 mile $\approx$ 1.60934 km (or 1 km $\approx$ 0.621371 miles)
* 1 gallon $\approx$ 3.78541 liters
* Step 1: Convert distance from km to miles.
$$300 \text{ km} \times \frac{1 \text{ mile}}{1.60934 \text{ km}} \approx 186.41 \text{ miles}$$
* Step 2: Calculate gallons needed.
$$\text{Gallons} = \frac{\text{Distance}}{\text{Efficiency}} = \frac{186.41 \text{ miles}}{25 \text{ miles/gallon}} \approx 7.456 \text{ gallons}$$
* Step 3: Convert gallons to liters.
$$7.456 \text{ gallons} \times 3.78541 \text{ L/gal} \approx 28.22 \text{ Liters}$$

Problem 4: If you can run 100 meters in 10 seconds, how long would it take you to run 100 yards?
* Given: Speed = 100m / 10s = 10 m/s. Target Distance = 100 yards.
* Goal: Time in seconds.
* Conversion Factors Needed:
* 1 meter $\approx$ 1.09361 yards (or 1 yard = 0.9144 meters)
* Step 1: Convert target distance to meters.
$$100 \text{ yards} \times 0.9144 \text{ m/yard} = 91.44 \text{ meters}$$
* Step 2: Calculate time.
$$\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{91.44 \text{ meters}}{10 \text{ m/s}} = 9.144 \text{ seconds}$$

Problem 5: If you can read 1 book every 2 hours, how many books could you read in a 30-day month if you read 4 hours a day?
* Given: Rate = 1 book / 2 hours. Daily reading time = 4 hours. Duration = 30 days.
* Goal: Total books.
* Calculation:
* First, find total hours spent reading: $30 \text{ days} \times 4 \text{ hours/day} = 120 \text{ hours}$.
* Next, calculate books: $\frac{120 \text{ hours}}{2 \text{ hours/book}} = 60 \text{ books}$.

Problem 6: You drive at an average speed of 60 mph. How far will you travel in 3 hours and 15 minutes?
* Given: Speed = 60 mph. Time = 3 hours 15 minutes.
* Goal: Distance.
* Conversion: Convert time to decimal hours.
* 15 minutes = $\frac{15}{60}$ hours = 0.25 hours.
* Total time = 3.25 hours.
* Calculation:
$$\text{Distance} = \text{Speed} \times \text{Time}$$
$$\text{Distance} = 60 \text{ mph} \times 3.25 \text{ hours}$$
$$\text{Distance} = 195 \text{ miles}$$

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Final Answer:
Here are the solutions to the problems on the worksheet:

1. Seconds in 50 years: Approximately 1,576,800,000 seconds (or $1.58 \times 10^9$ s).
2. Weeks in 2000 years: Approximately 104,286 weeks.
3. Liters needed for trip: Approximately 28.2 Liters.
4. Time to run 100 yards: Approximately 9.14 seconds.
5. Books read in a month: 60 books.
6. Distance traveled: 195 miles.