Considering Rocket A weighs twice as much as Rocket B, which statement about their kinetic energy is true?

The correct choice indicates that Rocket A has two times the kinetic energy of Rocket B, which is based on the relationship between mass and kinetic energy. Kinetic energy is expressed mathematically by the formula ( KE = \frac{1}{2} mv^2 ), where ( m ) is mass and ( v ) is velocity.

Since Rocket A weighs twice as much as Rocket B, we can represent the mass of Rocket B as ( m ) and the mass of Rocket A as ( 2m ). If both rockets are traveling at the same velocity ( v ), we can calculate their kinetic energies:

• For Rocket A:

[

KE_A = \frac{1}{2} (2m) v^2 = mv^2

]

• For Rocket B:

[

KE_B = \frac{1}{2} m v^2

]

By comparing the two results, we find that:

[

KE_A = 2 \times KE_B

]

This shows that Rocket A indeed has two times the kinetic energy of Rocket B when both are traveling at the same speed.

The understanding of this relationship is crucial in mechanics, as it illustrates