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
[tex]x_{Sh} = x_{o} + v_{Sh}\cdot t[/tex]
Submarine
[tex]x_{Su} = x_{o}+v_{Su}\cdot t[/tex]
Where:
[tex]x_{o}[/tex] - Position of Diego Garcia island, measured in miles.
[tex]x_{Sh}[/tex], [tex]x_{Su}[/tex] - Current positions of ship and submarine, measured in miles.
[tex]v_{Sh}[/tex], [tex]v_{Su}[/tex] - Velocities of ship and submarine, measured in miles per hour.
[tex]t[/tex] - TIme, measured in hours.
If we know that [tex]x_{Sh} - x_{Su} = 241\,mi[/tex], [tex]v_{Sh} = 19\,\frac{mi}{h}[/tex] and [tex]t = 7\,h[/tex], then:
[tex]x_{Sh} - x_{Su} = (v_{Sh}-v_{Su})\cdot t[/tex]
We clear now the velocity of submarine:
[tex]\frac{x_{Sh}-x_{Su}}{t} = v_{Sh}-v_{Su}[/tex]
[tex]v_{Su} = v_{Sh}-\frac{x_{Sh}-x_{Su}}{t}[/tex]
[tex]v_{Su} = 19\,\frac{mi}{h} -\frac{241\,mi}{7\,h}[/tex]
[tex]v_{Su} = -15.429\,\frac{mi}{h}[/tex]
Speed of the submarine is the magnitude of its velocity, which is 15.429 miles per hour.
