(a) [tex]4.7\cdot 10^9 J[/tex]
The kinetic energy of an object is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m is the mass of the object
v is its speed
For the ship in this problem,
[tex]m=7.00 \cdot 10^7 kg[/tex] is the mass
[tex]v = 11.6 m/s [/tex] is the speed
Substituting,
[tex]K=\frac{1}{2}(7.00 \cdot 10^7 kg)(11.6 m/s)^2=4.7\cdot 10^9 J[/tex]
(b) [tex]-4.7\cdot 10^9 J[/tex]
The work done on the ship is equal to the change in kinetic energy of the ship; so we have:
[tex]W = K_f - K_i[/tex]
where
W is the work done
Kf is the final kinetic energy of the ship, which is zero since it comes to rest
Ki is the initial kinetic energy of the ship, which is [tex]4.7\cdot 10^9 J[/tex]
Substituting into the formula,
[tex]W=0-4.7\cdot 10^9 J=-4.7\cdot 10^9 J[/tex]
and the sign is negative because the force used to stop the ship acts against the direction of motion of the ship, in order to slow it down.
(c) [tex]1.57\cdot 10^6 N[/tex]
The work done by the force applied to stop the ship is
W = Fd
where
W=-4.7\cdot 10^9 J is the work done
F is the force applied
d = 3.00 km = 3000 m is the displacement of the ship
Solving the equation for F, we find the force:
[tex]F=\frac{W}{d}=\frac{-4.7\cdot 10^9 J}{3000 m}=-1.57\cdot 10^6 N[/tex]
and ignoring the negative sign, the magnitude of the force is
[tex]1.57\cdot 10^6 N[/tex]
