Asteroid A has 3.5 times the mass and 2.0 times the velocity of Asteroid B. If Asteroid B has a kinetic energy of 2,300,000 J then what is the kinetic energy of
Asteroid A?

   K_A = 32.2 10⁶ J

Explanation:

In this exercise we must relate the quantities given to find the kinetic energy

Asteroid A data

              m_A = 3.5 m_B

               v_A = 2.0 v

they also give the value of the kinetic energy of asteroid A

              K_B = 2.3 10⁶ J

the expression for scientific energy is

               K = ½ m v²

let's replace

              K_A = ½ m_a V_a2

               K_A = ½ 3.5 m_B (2.0 v_B)^2

                K_A = 3.5 2² (½ m_B v_B²)

                K_A = 14 K_B

               K_A = 32.2 10⁶ J