Final answer:
The speed of a skater's outstretched hands while spinning at 130 rpm (with hands 130 cm apart) is approximately 884 cm/s, but this value does not match any of the provided options, indicating a potential issue with the question.
Step-by-step explanation:
The question concerns the calculation of the speed of a figure skater's hands while in a spinning motion. Assuming a skater spins at 130 revolutions per minute (rpm), we need to convert this to angular velocity in radians per second. Since 130 rpm is equivalent to 13.6 radians/second (because 1 rpm = 2π/60 radians/second), and the distance of each hand from the axis of rotation is 65 cm (130 cm apart), we can calculate the speed using the formula speed = angular velocity × radius.
To find her hands' speed, we multiply the angular velocity by the radius of one arm (half the total distance between them):
- Speed = 13.6 radians/second × 0.65 meters,
- Speed ≈ 8.84 m/s,
- Speed ≈ 884 cm/s (since 1 m = 100 cm).
However, since none of the given answer options (a) 130 cm/s, (b) 260 cm/s, (c) 390 cm/s, (d) 520 cm/s) match the calculated speed of 884 cm/s, there may be an error in the question or the provided options. If forced to choose the closest correct answer, option (d) 520 cm/s would be the closest to the calculated speed, albeit it is still not correct.