We have a very long train car moving in the positive x-direction with a speed of

Question

We have a very long train car moving in the positive x-direction with a speed of 9.95 m/s relative to the ground. At t = 0, a person on the train car is moving in the positive x-direction with a speed of 2.69 m/s relative to the train.
(a) What is the velocity of the person relative ground? m/s
The person is carrying a live paint grenade with a lifetime of 6.09 s. The grenade is activated at t = 0 seconds when the middle of the train car passes the origin of x-axis on the ground.
(b) How far does the person move relative to the train before he is covered with paint? m
(c) How far does the person move relative to the ground before he is covered with paint? m

Explanation / Answer

The speed of the train relative to the ground v = 9.95m/s

the speed of the person realtive to the train vr = 2.69m/s

(a) The velcoity of the person realtive to the ground

                v' = v + vr

                   = 9.95 + 2.69

                    = 12.64 m/s

(b) The person traveld a distance is

              x = vr *t = (2.69)(6.09)

                           = 16.38 m

(C) The distance traveled by person realtive to ground

           x =v'*t = (12.64)(6.09)

                     = 76.97 m

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