A car (mass 880 kg) is traveling with a speed of 44 mi/h. A bug (mass 7.9 mg) is traveling in the opposite direction. What speed would the bug need in order to slow down the truck by one mile per hour in a big bug splash (i.e., final speed 43 mi/h)?
The momentum of the bug before impact would have to be 1/44 of the car's momentum, and in the opposite direction.
Mc*Vc - Mb*Vb = (Mb+Mc)*(43/44)Vc
Vb = (Mc/Mb)*Vc - {(Mb+Mc)/Mb](43/44)Vc}
= 1.114*10^5*Vc - 1.089*10^5*Vc
= 0.025*10^5 Vc = 1.1*10^5 mph
Vc = car's initial speed
Vb = bug's initial speed