The most appropriate investigation method for the student to determine the effect of mass on kinetic energy is:
She should drop two balls with different masses from the same height.
This method allows her to isolate the variable of mass, while controlling for height, which is crucial since gravitational potential energy is converted to kinetic energy as the balls fall. By keeping the height the same, she can directly compare the kinetic energy of the two balls when they hit the water, attributing any differences in kinetic energy to their differing masses.