Which statement accurately compares the kinetic energy of two rockets descending at different rates?

The correct response is based on the relationship between velocity and kinetic energy. Kinetic energy is calculated using the formula ( KE = \frac{1}{2} mv^2 ), where ( m ) is mass and ( v ) is velocity. This signifies that the kinetic energy of an object is proportional to the square of its velocity.

If Rocket B is descending at a rate that is twice as fast as Rocket A, then the velocities can be represented as ( v_A ) and ( v_B = 2v_A ). Plugging these velocity values into the kinetic energy formula gives the following:

For Rocket A:

[ KE_A = \frac{1}{2} m v_A^2 ]

For Rocket B:

[ KE_B = \frac{1}{2} m (2v_A)^2 = \frac{1}{2} m (4v_A^2) = 2 m v_A^2 ]

When considering kinetic energy, this indicates that Rocket B has four times the kinetic energy of Rocket A, assuming both rockets have the same mass. Therefore, if Rocket B is indeed moving at twice the velocity of Rocket A, it will have four times the kinetic energy, making this