Question

boat a and boat b have the same mass. boat as velocity is three times greater than that of boat b. compared to the kinetic energy of boat b, the kinetic energy of boat a is one - third as much. three times as much. six times as much. nine times as much.

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity.

Step2: Let mass and velocity of boats

Let the mass of Boat A and Boat B be $m$ (since they have the same mass). Let the velocity of Boat B be $v_{B}=v$, then the velocity of Boat A is $v_{A} = 3v$.

Step3: Calculate kinetic energy of Boat B

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

Step4: Calculate kinetic energy of Boat A

$K_{A}=\frac{1}{2}m(3v)^{2}=\frac{1}{2}m\times9v^{2}=9\times(\frac{1}{2}mv^{2})$.

Step5: Compare kinetic energies

Since $K_{B}=\frac{1}{2}mv^{2}$ and $K_{A}=9\times(\frac{1}{2}mv^{2})$, $K_{A} = 9K_{B}$.

Answer:

D. nine times as much.