Answer to Question #292387 in Mechanics | Relativity for bookaddict

Question

A boy has a mass of 50 kg. He jumps at a speed of 2.5 m/s into a stationary boat which has a mass of 70 kg. Please calculate their speed (ignore friction).

Answer 1

Given:

$m_1=50\:\rm kg$

$v_1=2.5\:\rm m/s$

$m_2=70\:\rm kg$

$v_2=0\:\rm m/s$

The law of conservation of momentum says

$$m_1v_1+m_2v_2=(m_1+m_2)u$$

The final speed of a boat with a boy

$$u=\frac{m_1v_1+m_2v_2}{m_1+m_2}=\frac{50*2.5+70*0}{50+70}=1.0\:\rm m/s$$