Brain Teaser answer May 09 2007

The maximum speed of the frog will occur at the instant the spring returns to its original length.  The energy that was stored in the spring is converted to the kinetic energy of the frog.  The spring force is proportional to the compression, so if the force in the spring is zero at the start, and has a maximum value of kx when the spring is fully compressed, the average force is 1/2 kx.  This moves through the compression distance x, so the work done in compressing the spring is kx2/2.  The stored energy is converted to kinetic energy of the frog, mv2/2, where m is the mass of the frog.  So kx2/2 = mv2/2, hence v = x Ö(k/m).  With the data given, v = 0.025 Ö(100/0.01) = 2.5m/s.