Answer: Nine times as much
Explanation:
The kinetic energy of an object is given by the following equation:
[tex]K=\frac{1}{2}mV^{2}[/tex] (1)
Where:
[tex]K[/tex] is the kinetic energy
[tex]m[/tex] is the mass of the object
[tex]V[/tex] is the velocity of the object
Now, in this case we have two boats, A and B, which have the same mass [tex]m[/tex]. However, the velocity of boat A [tex]V_{A}[/tex] is three times greater than that of Boat B [tex]V_{B}[/tex]:
[tex]V_{A}=3V_{B}[/tex] (2)
With this in mind, let's write the kinetic energy for each boat:
Boat A:
[tex]K_{A}=\frac{1}{2}mV_{A}^{2}[/tex] (3)
Substituting (2) in (3):
[tex]K_{A}=\frac{1}{2}m(3V_{B})^{2}[/tex] (4)
[tex]K_{A}=9(\frac{1}{2}mV_{B}^{2})[/tex] (5)
Boat B:
[tex]K_{B}=\frac{1}{2}mV_{B}^{2}[/tex] (6)
Comparing (5) and (6) we can see the kinetic energy of boat A is nine times as much as the kinetic energy of boat B.
