A narrow treadmill of length 5.0 m is installed down the aisle of a commuter train that travels along a straight, horizontal track. The treadmill belt runs in the same direction as the train. The following simultaneous observations are made while all motions are steady (forward is defined as the train’s direction of travel):
• A security camera attached rigidly to the treadmill housing records the jogger’s speed to be 0.80 m/s forward relative to the treadmill belt.
• A seated passenger, who is at rest relative to the train car, measures the jogger’s speed to be 0.20 m/s forward relative to the train floor.
• An observer standing on the station platform measures the jogger’s speed to be 7.0 m/s forward relative to Earth.
All observers use a coordinate system in which the forward direction is positive.
(1) Using clearly defined symbols, write an equation that relates the jogger’s speed relative Earth to the jogger’s speed relative the treadmill belt, the belt’s speed relative the train, and the train’s speed relative Earth.
(2) Use the observations to determine the treadmill belt’s speed (magnitude and direction) relative to the train.
(3) Determine the train’s speed relative Earth.
(4) Explain the physical meaning of the sign of the belt’s speed that you found in part (b).