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: Write the 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 the velocity of Boat B be \(v_B\) and mass of both boats be \(m\)

For Boat B, \(K_B=\frac{1}{2}mv_B^{2}\). For Boat A, \(v_A = 3v_B\), so \(K_A=\frac{1}{2}m(3v_B)^{2}\).

Step3: Simplify the expression for \(K_A\)

\(K_A=\frac{1}{2}m\times9v_B^{2}=9\times(\frac{1}{2}mv_B^{2})\). Since \(K_B = \frac{1}{2}mv_B^{2}\), then \(K_A = 9K_B\).

Answer:

nine times as much.