Please help with these problems, I don't understand them. Thanks!
Suppose the circumference of a bicycle wheel is 2 meters. If it rotates at 1 revolution per second when you are riding the bicycle, then your speed will be?
Suppose you're on a Ferris wheel at a carnival, seated 10 m from the Ferris wheel's axis. If you make a complete rotation each minute, your linear speed is?
1rev/sec * 2meters/rev = what
1rotation/min* 10m*2*PI/rotation=what
Of course, I'd be happy to help you with these problems!
1) Let's start with the first problem about the bicycle wheel's speed. To find your speed, you need to know the circumference of the wheel and the number of revolutions per second.
Given:
- Circumference of the bicycle wheel = 2 meters
- Rotations per second = 1
To find your speed, multiply the circumference by the number of rotations per second. In this case, it will be:
Speed = Circumference * Rotations per second
Substituting the given values:
Speed = 2 meters * 1 rotation/second
Speed = 2 meters/second
Therefore, your speed when riding the bicycle will be 2 meters per second.
2) Now, let's move on to the second problem about the Ferris wheel's linear speed. To find your linear speed, you need to know the distance from the axis (radius) and the time it takes to make one rotation.
Given:
- Distance from the Ferris wheel's axis (radius) = 10 meters
- Time for one rotation = 1 minute
To find your linear speed, you need to convert the time to seconds. There are 60 seconds in one minute.
1 minute = 60 seconds
Now, convert the time to seconds:
Time = 1 minute * 60 seconds/minute
Time = 60 seconds
To find your linear speed, multiply the circumference of the circular path (2πr) by the reciprocal of the time taken for one rotation. In this case, it will be:
Linear Speed = Circumference of the circular path * 1 / Time
Substituting the given values:
Linear Speed = 2π * 10 meters * 1 / 60 seconds
Linear Speed ≈ 10.47 meters/second
Therefore, your linear speed when riding the Ferris wheel is approximately 10.47 meters per second.