Question

Plzz help! A stationary speed gun emits a

microwave beam at 2.41x1010 Hz. It
reflects off a pitched baseball and
returns 3190 Hz higher. What is the
speed of the baseball?
(Unit = m/s)

Answer 1

The speed of the baseball is approximately 19.855 m/s

Step-by-step 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;

`(\Delta f)/(f) = (2 \cdot v_(baseball))/(c)`

`\therefore{\Delta f}{} = (2 \cdot v_(baseball))/(c) * 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 = (2 \cdot v_(baseball))/(3.0 * 10^8 \ m/s) * 2.41 * 10^(10) \ Hz`

`v_(baseball) = (3190 \ Hz * 3.0 * 10^8 \ m/s )/(2.41 * 10^(10) \ Hz * 2) \approx 19.855 \ m/s`

The speed of the baseball,
`v_(baseball)` ≈ 19.855 m/s