You and your team are tasked with covertly acquiring information about a new helicopter being developed by

Question:

You and your team are tasked with covertly acquiring information about a new helicopter being developed by an adversary. You are given a handheld device that has many functions, one of which is to send out a broad pulse of electromagnetic waves at a frequency of f₀ = 9.00 × 10⁹ Hz, and then collect the scattered light that returns from whatever it hits. The device then analyzes the scattered light and returns a graph of maximum frequency shift as a function of collection angle (see the drawing). The device also has a built-in rangefinder that measures the distance to an object. As the helicopter engine powers up and the helicopter just starts to lift off the ground, you point the device at it and pull the trigger. It sends out a pulse and, a few seconds later, it gives you

(i) the distance to the helicopter (d = 82.7 m),

(ii) a graph of the frequency shift (Δf) versus collection angle, as shown in the figure.

(a) Assuming that light detected by your device has scattered from the moving rotor of the helicopter, what is the diameter of the rotor?

(b) What is the speed of the tips of the rotor?

Af (kHz) -5.35° +12.48 kHZ e (deg.) -12.48 kHZ +5.35°