A train is traveling with a speed of 50 miles/h with respect to the ground in the positive x-direction. A baseball player standing at the rear of the train pitches a baseball with a speed of 50 miles/h relative to the train off the back end, in the direction opposite the motion of the train. You are standing on the ground, observing the baseball. What is the velocity of the baseball at the moment of the throw that you observe

    v = 0

Explanation:

This is a relative velocity exercise, using the Galilean transformation

          v = v₁ + v '

where v₁ is the speed of the object with respect to the mobile system, v' the speed of the mobile system and v the speed of the object with respect to the fixed system.

We can also write this expression with subscripts

        v_at = v_am + v_mt

where v_at   velocity with respect to the ground

          v_am  speed respecting the mobile system

          v_mt   velocity of the mobile system with respect to the earth

System a mobile is the train with speed v ’= 50 mile / h

the speed of the ball with respect to the mobile system is v = - 50 mile / h

the velocity of the ball with respect to the fixed system is

         v = 50 -50

         v = 0

increases it