Question

Boat A and Boat B have the same mass. Boat A's velocity is three times greater than that of Boat B. Compared to

Answer 1

Answer: Nine times as much

Explanation:

The kinetic energy of an object is given by the following equation:

$K=\frac{1}{2}mV^{2}$ (1)

Where:

$K$ is the kinetic energy

$m$ is the mass of the object

$V$ is the velocity of the object

Now, in this case we have two boats, A and B, which have the same mass $m$. However, the velocity of boat A $V_{A}$ is three times greater than that of Boat B $V_{B}$:

$V_{A}=3V_{B}$ (2)

With this in mind, let's write the kinetic energy for each boat:

Boat A:

$K_{A}=\frac{1}{2}mV_{A}^{2}$ (3)

Substituting (2) in (3):

$K_{A}=\frac{1}{2}m(3V_{B})^{2}$ (4)

$K_{A}=9(\frac{1}{2}mV_{B}^{2})$ (5)

Boat B:

$K_{B}=\frac{1}{2}mV_{B}^{2}$ (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.