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

Answer:

$a = 0.308 m/s^2$

Explanation:

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

$F = \frac{dP}{dt}$

now we know that

$P = mv$

so we have

$F = v\frac{dm}{dt}$

$F = v \rhoA\frac{dx}{dt}$

$F = \rho A v^2$

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

$a = \frac{F}{m}$

$a = \frac{616000}{2 \times 10^6}$

$a = 0.308 m/s^2$