How many fluid ounces of pancake syrup (d = 1.78 g/mL) can be purchased for 35.00,giventhatthesyrupcosts1.05 per pound
The Correct Answer and Explanation is:
Here are the correct answers and a detailed explanation for each problem.
Answers:
d) 287 fluid ounces
e) 33.5 m/s
f) 2.03 x 10⁶ meters
Explanation:
d) How many fluid ounces of pancake syrup can be purchased?
This problem requires a multi step conversion process. First, determine the mass of syrup you can buy. With $35.00 and a cost of $1.05 per pound, you can purchase $35.00 / $1.05/lb = 33.33 pounds of syrup.
Next, convert this mass into grams to use the density value. Knowing that 1 pound is approximately 453.59 grams, the mass is 33.33 lbs × 453.59 g/lb ≈ 15118 g.
Now, use the syrup’s density (d = 1.78 g/mL) to find the volume. The formula is Volume = Mass / Density. So, the volume is 15118 g / 1.78 g/mL ≈ 8493 mL.
Finally, convert this volume from milliliters to fluid ounces. Since 1 fluid ounce is approximately 29.57 mL, the volume is 8493 mL / 29.57 mL/fl oz ≈ 287.2 fl oz. Rounding to three significant figures (from 1.05 and 1.78), the final answer is 287 fluid ounces.
e) Convert the speed limit into m/s.
To convert 75.0 miles per hour to meters per second, you need to convert both the distance unit (miles to meters) and the time unit (hours to seconds). We use a method called dimensional analysis.
First, let’s establish the conversion factors:
1 mile ≈ 1609.34 meters
1 hour = 3600 seconds
Now, set up the calculation so the unwanted units cancel out:
(75.0 miles / 1 hour) × (1609.34 meters / 1 mile) × (1 hour / 3600 seconds)
Multiplying the values gives:
(75.0 × 1609.34) / 3600 ≈ 33.5279 m/s.
The initial value, 75.0, has three significant figures, so the answer should also be rounded to three significant figures. This gives a final speed of 33.5 m/s.
f) How many meters will the projectile travel?
This problem asks for the total distance traveled in a given time. The projectile’s speed is 6.00 x 10³ feet per second, which is 6000 ft/s. The time is 18.5 minutes.
First, convert the time from minutes to seconds to match the units of the speed.
Time = 18.5 minutes × 60 seconds/minute = 1110 seconds.
Next, calculate the total distance traveled in feet using the formula: Distance = Speed × Time.
Distance = 6000 ft/s × 1110 s = 6,660,000 feet.
Finally, convert this distance from feet to meters. The conversion factor is 1 meter ≈ 3.28084 feet.
Distance = 6,660,000 feet / 3.28084 ft/m ≈ 2,030,000 meters.
Both given values (6.00 x 10³ and 18.5) have three significant figures. Therefore, the answer should be expressed in scientific notation with three significant figures as 2.03 x 10⁶ meters
