Question #324217

A runaway 185 kg wheeled skip is rolling east along a road with a velocity of +2.2 m s−1. A 2560 kg car moving to the west with a velocity of −9.7 m s−1 hits the skip.




After the collision the skip is moving west with a velocity of −14.4 m s−1.




What is the velocity of the car after the collision? (in m s−1 to 2 s.f)

1
Expert's answer
2022-04-11T12:04:37-0400

The law of conservation of momentum says

m1v1+m2v2=m1v1+m2v2m_1\vec v_1+m_2\vec v_2=m_1\vec v_1'+m_2\vec v_2'

Hence

m1v1m2v2=m1v1+m2v2m_1v_1-m_2 v_2=-m_1 v_1'+m_2 v_2'

v2=m1m2(v1+v1)v2v_2'=\frac{m_1}{m_2}(v_1+v_1')-v_2

v2=1852560(2.2+14.4)9.7=8.5  m/sv_2'=\frac{185}{2560}(2.2+14.4)-9.7=-8.5\;\rm m/s


The velocity of the car after the collision is directed westward.


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