Answer:
v_r = 1.268 × 10⁸ mi/hr
Explanation:
We are given;
wavelength of the red light; λr = 693 nm = 693 × 10^(-9) m
wavelength of the yellow light; λy = 582 nm = 582 × 10^(-9) m
Frequency is given by the formula;
f = v/λ
Where v is speed of light = 3 x 10^(8) m
Frequency of red light; f_o = [3 x 10^(8)]/(693 × 10^(-9)) = 4.33 x 10¹⁴ Hz
Similarly, Frequency of yellow light;
f = [3 x 10⁸]/(582 × 10^(-9)) = 5.15 x 10¹⁴ Hz
To find the speed of the car, we will use the formula;
f = f_o[(c + v_r)/c)]
Where c is speed of light and v_r is speed of car.
Making v_r the subject;
cf/f_o = c + v_r
v_r = c(f/f_o - 1)
So, plugging in the relevant values, we have;
v_r = 3 × 10⁸[((5.15 x 10¹⁴)/(4.33 x 10¹⁴)) - 1]
v_r = 3 × 10⁸(0.189)
v_r = 5.67 x 10⁷ m/s
Converting to mi/hr, 1 m/s = 2.23694 mile/hr
So, v_r = 5.67 × 10⁷ × 2.23694
v_r = 1.268 × 10⁸ mi/hr
