Question

determining change in kinetic energy
boat a and boat b have the same mass. boat a’s 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 (KE) is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

Step2: Define Variables for Boats

Let the mass of both Boat A and Boat B be $m$ (since they have the same mass). Let the velocity of Boat B be $v$, so the velocity of Boat A is $3v$ (as it is three times greater).

Step3: Calculate KE of Boat B

For Boat B, substitute into the KE formula: $KE_B = \frac{1}{2}m(v)^2=\frac{1}{2}mv^2$.

Step4: Calculate KE of Boat A

For Boat A, substitute $m$ and $3v$ into the KE formula: $KE_A = \frac{1}{2}m(3v)^2=\frac{1}{2}m\times9v^2 = 9\times(\frac{1}{2}mv^2)$.

Step5: Compare KE_A and KE_B

From Step 3, we know $\frac{1}{2}mv^2 = KE_B$. So $KE_A = 9\times KE_B$.

Answer:

nine times as much.