Answer:
The speed of the submarine is 15.429 miles per hour.
Step-by-step explanation:
Let suppose that both ships travel at constant velocities. As we know that both travel in opposite directions, it is supposed that cruise ship moves in +x direction, whereas submarine in -x direction. Kinematic equations for each sheep are described below:
Ship
![x_{Sh} = x_{o} + v_{Sh}\cdot t](https://tex.z-dn.net/?f=x_%7BSh%7D%20%3D%20x_%7Bo%7D%20%2B%20v_%7BSh%7D%5Ccdot%20t)
Submarine
![x_{Su} = x_{o}+v_{Su}\cdot t](https://tex.z-dn.net/?f=x_%7BSu%7D%20%3D%20x_%7Bo%7D%2Bv_%7BSu%7D%5Ccdot%20t)
Where:
- Position of Diego Garcia island, measured in miles.
,
- Current positions of ship and submarine, measured in miles.
,
- Velocities of ship and submarine, measured in miles per hour.
- TIme, measured in hours.
If we know that
,
and
, then:
![x_{Sh} - x_{Su} = (v_{Sh}-v_{Su})\cdot t](https://tex.z-dn.net/?f=x_%7BSh%7D%20-%20x_%7BSu%7D%20%3D%20%28v_%7BSh%7D-v_%7BSu%7D%29%5Ccdot%20t)
We clear now the velocity of submarine:
![\frac{x_{Sh}-x_{Su}}{t} = v_{Sh}-v_{Su}](https://tex.z-dn.net/?f=%5Cfrac%7Bx_%7BSh%7D-x_%7BSu%7D%7D%7Bt%7D%20%3D%20v_%7BSh%7D-v_%7BSu%7D)
![v_{Su} = v_{Sh}-\frac{x_{Sh}-x_{Su}}{t}](https://tex.z-dn.net/?f=v_%7BSu%7D%20%3D%20v_%7BSh%7D-%5Cfrac%7Bx_%7BSh%7D-x_%7BSu%7D%7D%7Bt%7D)
![v_{Su} = 19\,\frac{mi}{h} -\frac{241\,mi}{7\,h}](https://tex.z-dn.net/?f=v_%7BSu%7D%20%3D%2019%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D%20-%5Cfrac%7B241%5C%2Cmi%7D%7B7%5C%2Ch%7D)
![v_{Su} = -15.429\,\frac{mi}{h}](https://tex.z-dn.net/?f=v_%7BSu%7D%20%3D%20-15.429%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D)
Speed of the submarine is the magnitude of its velocity, which is 15.429 miles per hour.