Question

A speeding car is pulling away from a police car. The police car is moving at 30 m/s. The radar gun in the police car emits an electromagnetic wave with a frequency of 20.0 x 109 Hz. The wave reflects from the speeding car and returns to the police car where the frequency is measured to be 4750 Hz less than what was emitted. The speed of light is 3 x 108 m/s. How fast is the speeding car going?

Answer 1

Answer:

65.625 m/s

Explanation:

$F=20\times 10^9 Hz$

$\Delta F=F_r-F_t=4750 Hz$

c = Speed of light = 3×10⁸ m/s

Relative speed

$v=\frac{\Delta F}{2F}\times c\\\Rightarrow v=\frac{4750}{2\times 20\times 10^9}\times 3\times 10^8\\\Rightarrow v=35.625\ m/s$

Relative speed = 35.625 m/s

Velocity of speeder = Velocity of police car + Relative speed

⇒Velocity of speeder = 30 + 35.625 = 65.625 m/s

∴ Velocity of speeder is 65.625 m/s