Question

Plzz help! A stationary speed gun emits a

Answer 1

Answer:

The speed of the baseball is approximately 19.855 m/s

Explanation:

From the question, we have;

The frequency of the microwave beam emitted by the speed gun, f = 2.41 × 10¹⁰ Hz

The change in the frequency of the returning wave, Δf = +3190 Hz higher

The Doppler shift for the microwave frequency emitted by the speed gun which is then reflected back to the gun by the moving baseball is given by 2 shifts as follows;

 $\dfrac{\Delta f}{f} = \dfrac{2 \cdot v_{baseball}}{c}$

$\therefore{\Delta f}{} = \dfrac{2 \cdot v_{baseball}}{c} \times f$

Where;

Δf = The change in frequency observed, known as the beat frequency = 3190 Hz

$v_{baseball}$ = The speed of the baseball

c = The speed of light = 3.0 × 10⁸ m/s

f = The frequency of the microwave beam = 2.41 × 10¹⁰ Hz

By plugging in the values, we have;

$\therefore{\Delta f} = 3190 \ Hz = \dfrac{2 \cdot v_{baseball}}{3.0 \times 10^8 \ m/s} \times 2.41 \times 10^{10} \ Hz$

$v_{baseball} = \dfrac{3190 \ Hz \times 3.0 \times 10^8 \ m/s }{2.41 \times 10^{10} \ Hz \times 2} \approx 19.855 \ m/s$

The speed of the baseball, $v_{baseball}$ ≈ 19.855 m/s