A person riding on the roof of a freight train throws a ball forward. (a) Neglecting air drag and relative to the ground, is the ball moving faster or slower when the train is moving than when it is standing still? (b) Relative to the freight car, is the ball moving faster or slower when the train is moving than when the train is standing still?

Solution Step 1 of 3 In question 1, Here since the speeds are very less compared to speed of light, we can use normal velocity vector addition; The speed of the ball thrown forward from the top of train with respect to ground (neglecting air resistance) v ballground vtrainground vballtrain……….1 Where v ballgrounds the speed of ball relative to ground v is the speed of train relative to ground trainground v is the speed of ball relative to train balltrain Step 2 of (a) Neglecting air drag and relative to the ground, is the ball moving faster or slower when the train is moving than when it is standing still When the train is at rest v trainground0 From above equation, Speed of ball relative to ground when it is at rest, vballground= 0 + vballtrain vballground(rest)vballtrain…..2 When the train is moving, v traingroundfinite value From above equation, Speed of ball relative to ground when train is moving, vballground(moving)vtrainground vballtrain…...3 Therefore comparing equation 3 and 2 v >v ballground(moving) ballground(rest) That is, the speed of ball relative to ground is greater when the train is moving than when the train is at rest.