Final answer:
The speeds of the tips of the main and tail rotors of a single-engine helicopter are found by converting the revolutions per minute to radians per second and multiplying by the rotor radius. The main rotor tip speed is approximately 351.86 m/s, and the tail rotor tip speed is about 369.14 m/s.
Step-by-step explanation:
To find the speeds of the tips of each rotor on a single-engine helicopter, we need to use the relationship between linear speed and angular speed. The linear speed (v) of a point on a rotating object is given by the product of the angular speed (ω) in radians per second and the radius (r) of the circle that the point is tracing out, which is half of the rotor diameter. The formula is v = ωr.
We first convert the main rotor's rotation rate from revolutions per minute (rev/min) to radians per second (rad/s). 480 rev/min is equivalent to 480 * 2π rad/60 s or 50.265 rad/s. The main rotor's radius is half of its diameter, 14 m / 2 = 7 m. Thus, the speed of the tips of the main rotor is v = 50.265 * 7 m/s. This gives a speed of approximately 351.86 m/s.
Similarly, the tail rotor rotates at 3750 rev/min, which is equivalent to 3750 * 2π rad/60 s or approximately 392.7 rad/s. Its radius is 1.88 m / 2 = 0.94 m. The speed of the tips of the tail rotor is, therefore, v = 392.7 * 0.94 m/s. This results in a speed of about 369.14 m/s.