- #1

brotherbobby

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- Homework Statement
- Two landing stakes ##\text{M}## and ##\text{N}## are served by launches that all travel at the same speed relative to water. The distance between the landing stages is ##20\;\text{km}##. It is covered by each launch from ##\text{M}## to ##\text{N}## in one hour and from ##\text{N}## to ##\text{M}## in two hours. The launches leave the two landing stages at the same time at an interval of 20 minutes and stop at each of them also for 20 minutes.

Determine :

(1) The number of launches in service.

(2) The number of launches met by a launch travelling from ##\text{M}## to ##\text{N}##.

(3) The number of launches met by a launch travelling from ##\text{N}## to ##\text{M}##.

- Relevant Equations
- Relative velocity of A with respect to B : ##v_{AB}= v_{AC}-v_{BC}##

**I start by compying and pasting the problem as it appeared in the text. Please note that for reasons of clarity, I replaced landing station ##\text{K}## with station ##\text{N}##.
Attempt : **

[I could not answer the questions asked, but let me show you what I

__could__do. Given how little it is, any help is welcome]

The time taken in the forward direction ##t_F=\dfrac{d}{v_F}=\dfrac{d}{v_L+v_R}##, where ##v_L## is the velocity of the launch. Hence ##1= \dfrac{20}{v_L+v_R}\Rightarrow v_L+v_R=20\qquad (1)##

Likewise, ##t_B=\dfrac{d}{v_B}=\dfrac{d}{v_L-v_R}\Rightarrow 2= \dfrac{20}{v_L-v_R}\Rightarrow v_L-v_R=10\qquad (2)##.

Solving (1) and (2), ##v_L=15\;\text{km/h}## and ##v_R=5\;\text{km/h}##.

I don't know how to proceed from here to answer questions (1) - (3).

Any help or suggestion is welcome.

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