A subcompact car, mass 1,000 kg, runs into and sticks to an at-rest, 2,200 kg SUV. lf their final speed is 4.7 m/s, what was the smaller car's initial speed?

1 Answer
hereyougo
Feb 21, 2018

15.04 m/s

Explanation:

First, because of the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

#p_(sc) =# initial momentum of the subcompact car
note that the initial momentum of the SUV is 0 because it is at rest.
#p_(suv)' =# final momentum of the SUV
#p_(sc)' =# final momentum of the subcompact car.
also note that the final velocities of the cars are the same so that will be denoted as #v'#

#p_(sc) = p_(sc)' + p_(suv)'#
#(m_(sc))(v_(sc)) = (m_(sc))(v')+(m_(suv))(v')#

solve for #v_(sc)#

#v_(sc)= ((m_(sc))(v')+(m_(suv))(v'))/(m_(sc))#

plug in numbers

#v_(sc) = (1000*4.7+2200*4.7)/1000#
#v_(sc) = 15.04# m/s

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