Two objects, A and B, have the same kinetic energy. A has a speed that is 11.4 times greater than the speed of B. What is the ratio of the mass of B to the mass of A?

Question

Two objects,  A and  B,  have the same kinetic energy.  A has a speed that is 11.4 times greater than the speed of B. What is the ratio of  the mass of B to the mass of A?

anonymous · Answer

kinetic energy (KE) =(1/2)m(v^2)

velocity of object A = 11.4 * (velocity of object B)

KE of A = KE of B

KE of A = (1/2)(mass of A)(velocity of object A)^2
              = (1/2)(mass of B)(velocity of object B * 11.4)^2

KE of B = (1/2)(mass of B)(velocity of object B)^2

Divide the two kinetic energy equations, left hand side = 1. I guess you can find the ratio now.