# Basic Equations (1) – Rocking the boat

Here’s a picture of a rower, just to explain the basic concepts. Click on the image to see a full size version. The system consists of a crew with its mass $m_c$ and a boat with its mass $m_b$.

The entire system is moving with a velocity $v_t$ with respect to the viewer on the dock. However, the crew is moving with respect to the boat, and as a consequence (conservation of momentum) the boat itself moves at a higher speed $v_t + v_b$. The crew velocity is $v_t + v_b - v_c$.

Conservation of momentum gives us:

$m_c (v_t + v_b - v_c) + m_b (v_t + v_b) = m_c v_t + m_b v_t$

So, we can derive what you do to your shell speed by racing the recovery:

$v_b = \frac{m_c}{m_c + m_b} v_c$