An instrument shows the number of revolutions per
minute made by each tire of a car. In each revolution, the
car travels a distance equal to the circumference of one of
its tires. The circumference of each tire is equal to 2πr,
where r is the radius of the tire.
If the radius of each tire on Maria’s car is 0.30 meter,
what is the approximate speed of Maria’s car, to the
nearest kilometer per hour, when the instrument is
showing 779 revolutions per minute?
(1 kilometer = 1000 meters)
tire circumference * rpm * minutes per hour / meters per km
2 * π * 0.30 * 779 * 60 / 1000
C = 2pi*r = 6.28 * 0.3 = 1.884 m/rev. = Circumference.
Speed = 779rev/min * 1.884m/rev. * 1km/1000m * 60min/h = 88 km/h.
To find the approximate speed of Maria's car, we need to determine the distance traveled in one minute and then convert it to kilometers per hour.
1. First, let's find the distance traveled in one revolution of the tire.
The circumference of each tire is equal to 2πr, where r is the radius of the tire.
Given that the radius of each tire is 0.30 meters, the circumference of each tire is:
Circumference = 2πr = 2 * π * 0.30 ≈ 1.88496 meters (rounded to 5 decimal places)
2. Next, let's determine the distance traveled in one minute.
Since the car makes 779 revolutions per minute, the total distance traveled in one minute is:
Distance in one minute = 779 * Circumference ≈ 779 * 1.88496 ≈ 1470.20584 meters (rounded to 5 decimal places)
3. Finally, let's convert the distance traveled in one minute to kilometers per hour.
We know that 1 kilometer is equal to 1000 meters, and 1 hour is equal to 60 minutes.
To convert the distance in meters to kilometers, divide by 1000:
Distance in kilometers = 1470.20584 / 1000 ≈ 1.47020 kilometers (rounded to 5 decimal places)
Now, to convert the distance from minutes to hours, divide by 60:
Speed in kilometers per hour = 1.47020 / (1/60) ≈ 1.47020 * 60 ≈ 88.212 kilometers per hour (rounded to 3 decimal places)
Therefore, the approximate speed of Maria's car, to the nearest kilometer per hour, when the instrument is showing 779 revolutions per minute, is approximately 88 kilometers per hour.
To find the approximate speed of Maria's car, we need to calculate the distance covered by the car in one minute and then convert it to kilometers per hour.
1. Calculate the distance covered by the car in one revolution:
The circumference of each tire is equal to 2πr, where r is the radius of the tire.
Given that the radius of each tire is 0.30 meters, the circumference of each tire is:
Circumference = 2π(0.30) = 1.89 meters.
2. Calculate the distance covered by the car in one minute:
The car travels a distance equal to the circumference of one of its tires in each revolution.
When the instrument shows 779 revolutions per minute, the distance covered by the car in one minute is:
Distance = 1.89 meters/revolution × 779 revolutions/minute = 1472.31 meters/minute.
3. Convert the distance to kilometers per hour:
We know that 1 kilometer is equal to 1000 meters, and 1 hour is equal to 60 minutes.
To convert the speed from meters per minute to kilometers per hour, we can use the following conversion factors:
1 kilometer/1000 meters and 60 minutes/1 hour.
Distance in kilometers per hour = 1472.31 meters/minute × (1 kilometer/1000 meters) × (60 minutes/1 hour)
= 88.39 kilometers per hour.
Therefore, the approximate speed of Maria's car, to the nearest kilometer per hour, when the instrument is showing 779 revolutions per minute, is approximately 88 kilometers per hour.