Worked example: A train moves at v = 20 m/s. A passenger walks forward at u′ = 2 m/s relative to the train. A ball is dropped from the passenger's hand. Describe the motion in both frames. Step 1: In the train frame S′, the ball has horizontal velocity 0 (released from rest) and falls straight down with acceleration g. Step 2: Galilean transformation to the ground frame S: x = x′ + vt, so horizontal velocity u = u′ + v = 0 + 20 = 20 m/s. Step 3: In the ground frame the ball follows a parabola: x = 20t, y = −½gt². Step 4: Time is absolute: t′ = t, so both frames agree the ball takes the same time to hit the floor. Conclusion: the trajectory looks different (straight vs parabolic) but the law — projectile motion under gravity — is identical in both inertial frames.