A boy is twirling a model plane on a string that is 2 meters long. If he twirls the plane at 0.4 revolutions per second, how far does the plane travel in 5 minutes? Give your answer in meters to 2 decimal places.
To find out how far the plane travels in 5 minutes, we need to calculate the total number of revolutions it completes in that time period.
1. First, convert 5 minutes to seconds: 5 minutes * 60 seconds/minute = 300 seconds
2. Next, calculate the total number of revolutions completed in 300 seconds:
Revolutions = 0.4 revolutions/second * 300 seconds = 120 revolutions
3. Since the length of the string is 2 meters, the plane travels 2 meters in one revolution.
4. Finally, calculate the total distance travelled by multiplying the number of revolutions by the distance per revolution:
Distance = 2 meters/revolution * 120 revolutions = 240 meters
Therefore, the model plane travels 240 meters in 5 minutes.
To find out how far the plane travels in 5 minutes, we need to determine the distance covered in each revolution and then multiply it by the total number of revolutions.
First, let's calculate how many revolutions the plane makes in 5 minutes. There are 60 seconds in a minute, so there are 5 × 60 = 300 seconds in 5 minutes.
Next, we need to determine the distance covered in one revolution. The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. Here, the length of the string is the radius of the circle.
The length of the string is 2 meters, so the radius is also 2 meters. Therefore, the distance covered in one revolution is 2π × 2 = 4π meters.
Now, let's calculate the total distance covered by multiplying the distance covered in one revolution by the total number of revolutions:
Total distance = Distance per revolution × Total number of revolutions
Total distance = 4π meters × (0.4 revolutions per second × 300 seconds)
Calculating that expression gives us:
Total distance = 4π × 0.4 × 300 meters
Now, to find the final answer:
Total distance = 4π × 0.4 × 300 meters
Using the value π ≈ 3.14:
Total distance ≈ 3.14 × 0.4 × 300 meters
Total distance ≈ 376.8 meters
Therefore, the plane travels approximately 376.8 meters in 5 minutes.
c = 2πr, so one revolution of the plane travels 4π meters
So, now we know that
5 min * 60s/min * 0.4rev/s * 4πm/rev = (5*60*4π)/(0.4) = 300π meters