A motorcycle stunt rider plans to start from one end of a railroad flatcar, acce

Question

A motorcycle stunt rider plans to start from one end of a railroad flatcar, accelerate toward the other end of the car, and jump from the flatcar to a platform. The motorcycle and rider have a mass of 303 kg and a length of 2.21 m. The flatcar has a mass of 1870 kg and a length of 20.1 m. Assume that there is negligible friction between the flatcar's wheels and the rails and that the motorcycle and rider can move through the air with negligible resistance. The flatcar is initially touching the platform. The promoters of the event have asked you how far the flatcar will be from the platform when the stunt rider reaches the end of the flatcar. What is your answer? 

Explanation / Answer

mass of rider m = 303kg mass of flat car M =1870 kg

if motorcycle speed is V towards right then flatcar speed is mV/M towards left

motor cycle speed with respect to flat car is V+mV/M

time taken by motor cycle to reach end of flat car = (20.1 m-2.21 m) /( V + mV/M )

distance travelled by flat car = speed x time = mV/M x (20.1 m-2.21 m) /( V + mV/M )
                                                                  = 17.89 x m/ (m +M)
                                                                  = 17.89 m x 303 kg / (303 kg + 1870 kg)
                                                                  = 2.49 m

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