Answer:
[tex]a = 0.308 m/s^2[/tex]
Explanation:
As we know that the force due to propeller when it will push the water backwards is given as
[tex]F = \frac{dP}{dt}[/tex]
now we know that
[tex]P = mv[/tex]
so we have
[tex]F = v\frac{dm}{dt}[/tex]
[tex]F = v \rhoA\frac{dx}{dt}[/tex]
[tex]F = \rho A v^2[/tex]
here we know that
[tex]A = \pi r^2[/tex]
[tex]A = \pi(7^2)[/tex]
[tex]A = 154 m^2[/tex]
now the force is given as
[tex]F = (1000)(154)(2^2)[/tex]
[tex]F = 616000 N[/tex]
now the acceleration of the ship is given by Newton's II law
[tex]a = \frac{F}{m}[/tex]
[tex]a = \frac{616000}{2 \times 10^6}[/tex]
[tex]a = 0.308 m/s^2[/tex]
