Answer
The recoil speed of the frog and lily pad is $1.2~cm/s$
Work Step by Step
We can assume the initial momentum of the tongue, frog, and lily pad is zero. By conservation of momentum, if the frog's tongue gains a certain momentum $p_t$ in one direction, the frog and lily pad will gain the same magnitude of momentum $p_f$ in the opposite direction.
We can find the recoil speed $v_r$ of the frog and lily pad:
$p_f = p_t$
$m_f~v_r = m_t~v_t$
$v_r = \frac{m_t~v_t}{m_f}$
$v_r = \frac{(4.1\times 10^{-5}~kg)(3.7~m/s)}{0.0125~kg}$
$v_r = 0.012~m/s = 1.2~cm/s$
The recoil speed of the frog and lily pad is $1.2~cm/s$.
