Question

Consider a ship of mass 2 x 10^6 kg with propeller blades of radius 7 m and it can push water backwards to a speed of 2 m/s. Given that the density of water is 1000 kg/m^3 , find the acceleration of the ship. (required answer is 0.308 m/s)

Answer 1

`a = 0.308 m/s^2`

Step-by-step explanation:

As we know that the force due to propeller when it will push the water backwards is given as

`F = (dP)/(dt)`

now we know that

`P = mv`

so we have

`F = v(dm)/(dt)`

`F = v \rhoA(dx)/(dt)`

`F = \rho A v^2`

here we know that

`A = \pi r^2`

`A = \pi(7^2)`

`A = 154 m^2`

now the force is given as

`F = (1000)(154)(2^2)`

`F = 616000 N`

now the acceleration of the ship is given by Newton's II law

`a = (F)/(m)`

`a = (616000)/(2 * 10^6)`

`a = 0.308 m/s^2`