Which two choices define a frame of reference?
A passenger stands up on a moving train and walks toward the front at 1 m/s. The seated passenger beside him measures his velocity: 1 m/s forward. Someone standing on the ground as the train passes measures it too: 21 m/s forward. Who is right?
Both observers measure from a frame of reference: a chosen origin and a positive direction. The seated passenger and the person on the ground carry different frames. The train is the seated passenger's frame; the ground is the other observer's.
From the seated passenger's frame, the walker gains 1 m/s on everything in the train car. The seated passenger measures 1 m/s forward.
From the ground frame, the train carries the walker forward at 20 m/s, and his own walking adds 1 m/s more. The ground observer measures:
20 m/s + 1 m/s = 21 m/s forward
So neither measurement is a mistake. Each observer's number is correct in that observer's frame. There is no secret third number that is the walker's one true velocity.
A waiter walks toward the front of a dining car at 1.0 m/s while the train travels at 24 m/s. Which velocity does a seated passenger in the dining car measure for the waiter?
To predict an observer's measurement, start from the mover's velocity inside the carrying frame. Then add the carrying frame's own velocity if the observer stands outside it.
A crew member walks toward the front of a river boat at 2 m/s while the boat moves at 10 m/s. Calculate the velocity an observer on the riverbank measures for the crew member.
Write down the values in the question:
crew member's velocity in the boat's frame = 2 m/s forward
boat's velocity in the riverbank's frame = 10 m/s forward
riverbank measurement = ?
The walk and the boat's motion point the same way, so the velocities add:
10 m/s + 2 m/s = 12 m/s
The observer on the riverbank measures 12 m/s forward.
An airport walkway glides at 2.0 m/s. A traveler on it walks forward at 1.5 m/s. Enter the velocity a person standing in the terminal measures for the traveler, in m/s.
A walk toward the rear points against the train's motion. So a rearward walk takes away from the carrying frame's speed instead of adding to it.
A boy walks toward the rear of a bus at 1 m/s while the bus drives at 15 m/s. Calculate the velocity a person on the sidewalk measures for the boy.
Write down the values in the question:
boy's velocity in the bus's frame = 1 m/s toward the rear
bus's velocity in the sidewalk's frame = 15 m/s forward
sidewalk measurement = ?
The walk points against the bus's motion, so it takes away from the bus's speed:
15 m/s − 1 m/s = 14 m/s
The person on the sidewalk measures 14 m/s forward.
A jogger runs down a riverside path. A passenger seated on a passing river boat and a person standing on the bank measure different velocities for the jogger. Why do the two measurements differ?
A flight attendant walks toward the front of a plane at 1.2 m/s while the plane flies at 240 m/s. Enter the velocity an observer on the ground measures for the flight attendant, in m/s.
A subway train travels at 12.0 m/s. A rider on board walks toward the rear at 1.0 m/s. Enter the velocity a person standing on the platform measures for the rider, in m/s.
A surfer rides a wave toward the beach. A drone flying alongside at the surfer's own velocity measures 0 m/s for the surfer; a camera operator on the beach measures 8 m/s. Which statement is true?