Final answer:
Let the masses of bodies A and B be 5x and x, respectively. Let the velocities of bodies A and B be vA and vB, respectively. The ratio of their velocities is vA/vB = sqrt(5/3).
Step-by-step explanation:
Let the masses of bodies A and B be 5x and x, respectively. Let the velocities of bodies A and B be vA and vB, respectively. The kinetic energy of a body is given by the equation KE = 0.5mv2.
Given that the masses are in the ratio 5:1 and the kinetic energies are in the ratio 125:9, we can set up the following equations:
1. 5x/125 = x/9 (equating the ratios of masses)
2. (0.5)(5x)(vA)2/125 = (0.5)(x)(vB)2/9 (equating the ratios of kinetic energies)
Simplifying equation 1 gives x = 25, and substituting this value into equation 2 allows us to solve for the ratio of velocities: vA/vB = sqrt((5x/125)/(x/9)) = sqrt(5/3).