Two objects, A and B, have the same kinetic energy. A has a speed that is 12.1 times greater than the speed of B. What is the ratio of the mass of B to the mass of A?

Question

I'm not sure how to do this one given... KE_A = KE_B & V_A = 12.1V_B

How do I find the ratio of the mass??

Answer 1

Notice that the problem says that the velocity of object A is 12.1 times GREATER than B:

Va = Vb + 12.1Vb = 13.1Vb.

Ma = Mass of object A.
Va = Velocity of object A.

Mb = Mass of object B.
Vb = Velocity of object B.

KE = Mb*(Vb)^2/2 = Ma*(13.1Vb)^2/2,
Mb*(Vb)^2/2 = Ma^(13.1Vb)^2,
Multiply both sides by 2:
Mb*(Vb)^2 = Ma*(13.1Vb)^2,
Divide both sides by (Vb)^2:
Mb = Ma*(13.1)^2,
Divide both sides by Ma:
Mb / Ma = (13.10^2 = 171.6m/s.