Final answer:
The maximum speed of the hummingbird's wing tip, which moves in simple harmonic motion, can be calculated using the formula v_max = 2πfA. With a frequency of 40 Hz and a total motion distance of 2.7 cm, the maximum speed is approximately 3.402 m/s.
Step-by-step explanation:
Calculating the Maximum Speed of a Hummingbird's Wing Tip
To calculate the maximum speed of a hummingbird's wing tip during its simple harmonic motion, we can use the formula for the maximum speed (vmax) in simple harmonic motion: vmax = 2πfA, where f is the frequency and A is the amplitude.
The amplitude (A) is half of the total distance of the motion, so A = 2.7 cm / 2 = 1.35 cm = 0.0135 m. The frequency (f) given is 40 Hz.
Using the formula:
vmax = 2π × 40 Hz × 0.0135 m
vmax = 2π × 40 × 0.0135 m/s
vmax = 3.402 m/s (rounded to three decimal places)
Therefore, the maximum speed of the wing tip is approximately 3.402 m/s.