- #1
brotherbobby
- 699
- 163
- 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 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.
Last edited: