(a)
The radial velocity components of both batches of raindrops.
(a)
Answer to Problem 69AP
The radial velocity components of first batch of raindrops is
Explanation of Solution
The first batch of raindrops are moving towards the radio station.
Here there is relative motion between the raindrop and the station. So apply Doppler’s equation to the situation.
Write the expression for the enhanced frequency of radio waves received by the first batch of raindrops.
Here,
The radio waves transmitted towards the first batch of raindrop gets reflected towards the radio station. There is an upward Doppler shift in the frequency of the reflected wave.
Write the expression for the enhanced frequency of the reflected radio waves from first batch of rain drops.
Here,
Use expression (I) in (II).
Due to the relative motion of rain drops and the pulse,
Write the expression to find
Here,
Use expression (IV) in (III).
Solve expression (V) for
Simplify expression (VI) to find
Take terms containing
Similarly repeat the calculations for the second batch of raindrops also. Here the frequency is enhanced in down ward direction. So replace
Conclusion:
Substitute
Substitute
Therefore, the radial velocity components of first batch of raindrops is
(b)
Angular speed of rotation of rotation of the rain drops.
(b)
Answer to Problem 69AP
The angular speed of rotation of the rain drops is
Explanation of Solution
The first batch of rain drops is at bearing of
The time taken by the radio wave to travel from station to rain and come back is
Write the expression for one way distance travelled by the radio waves.
Here,
Write the expression for the diameter of the vortex where the rain drops are whirling.
Here,
Write the expression for the angular sped of rotation of rain drop about the vortex in terms of the diameter.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the angular speed of rotation of the rain drops is
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Chapter 39 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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