Question #292387

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).


1
Expert's answer
2022-01-31T07:33:43-0500

Given:

m1=50kgm_1=50\:\rm kg

v1=2.5m/sv_1=2.5\:\rm m/s

m2=70kgm_2=70\:\rm kg

v2=0m/sv_2=0\:\rm m/s


The law of conservation of momentum says

m1v1+m2v2=(m1+m2)um_1v_1+m_2v_2=(m_1+m_2)u

The final speed of a boat with a boy

u=m1v1+m2v2m1+m2=502.5+70050+70=1.0m/su=\frac{m_1v_1+m_2v_2}{m_1+m_2}=\frac{50*2.5+70*0}{50+70}=1.0\:\rm m/s


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