Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions mix the five essential knowledge threads of Topic 1.4 — how the choice of reference frame determines what's measured, converting measurements between frames, combining an object's velocity with its observer's frame velocity, combining velocities with vector addition and subtraction (including in two dimensions), and why acceleration is the same as measured from any inertial reference frame. Unless stated otherwise, assume every reference frame in this assignment is inertial.
A ball sits motionless on the floor of a train car moving at 20 m/s relative to the ground. A passenger seated next to the ball measures its velocity as 0 m/s. An observer standing on the platform measures its velocity as 20 m/s. Which statement best describes this situation?
Select A, B, C, or D to check your answer.
A passenger on a train and a friend standing on the platform are each asked how fast the passenger is moving. The passenger says 0 m/s; the friend says 20 m/s (the train's speed). Explain why both answers are correct, and explain what this reveals about the idea of an object's single "true" or "absolute" velocity.
Two cars travel side by side down a highway, each at 25 m/s relative to the ground. What is Car B's velocity relative to Car A's driver?
Select A, B, C, or D to check your answer.
Car A travels east at 10 m/s (ground frame). Car B travels east at 25 m/s (ground frame) on the same road. Find Car A's velocity relative to Car B, and explain why its direction differs from Car A's own ground-frame direction.
A passenger stands still on a moving walkway that carries people forward at 1.5 m/s relative to the ground. Taking the walkway's starting point as the ground-frame origin, what is the passenger's ground-frame position after 10 s?
Select A, B, C, or D to check your answer.
A passenger walks forward at 1 m/s relative to the same moving walkway (which still moves at 1.5 m/s relative to the ground). (a) Find the passenger's position relative to the ground after 10 s. (b) In general, what information do you need to know in order to convert a measurement from one reference frame into another?
In general, what information must you know in order to convert a position or velocity measurement from one observer's reference frame into another observer's reference frame?
Select A, B, C, or D to check your answer.
A train moves down a straight track. At a certain moment, the train's own reference-frame origin (the front of the car) has traveled 50 m past the ground-frame origin (the station). A piece of luggage happens to be sitting exactly at the train's origin at that same moment. (a) What is the luggage's position in the ground frame at that moment? (b) What piece of information about the two frames did you need to answer part (a)?
A train moves at 20 m/s (ground frame). A passenger rolls a ball forward (same direction as the train's motion) at 2 m/s relative to the train floor. What is the ball's velocity relative to the ground?
Select A, B, C, or D to check your answer.
Same train (20 m/s forward, ground frame). This time the passenger rolls the ball backward (opposite the train's motion) at 5 m/s relative to the train floor. Find the ball's velocity relative to the ground, and explain why it's still directed forward overall.
A moving walkway carries people forward at 1.5 m/s relative to the ground. A passenger walks backward on it at 2 m/s relative to the walkway. What is the passenger's velocity relative to the ground?
Select A, B, C, or D to check your answer.
A swimmer swims upstream (against the current) at 1.2 m/s relative to the water. The river's current flows downstream at 2 m/s relative to the shore. Explain, using vector addition of velocities, why the swimmer ends up drifting downstream relative to the shore even though they are actively swimming upstream — and find their velocity relative to the shore.
A boat points straight across a river, moving at 4 m/s relative to the water. The river's current flows at 3 m/s, perpendicular to the boat's heading. What is the boat's speed relative to the ground (the riverbank)?
Select A, B, C, or D to check your answer.
A plane has an airspeed of 200 km/h, heading due north, relative to the surrounding air. A wind blows at 50 km/h due east. (a) Find the plane's velocity components relative to the ground. (b) Find the magnitude of its ground velocity.
Car A travels east at 25 m/s (ground frame). Car B travels east at 15 m/s (ground frame) on the same road. What is Car A's velocity relative to Car B?
Select A, B, C, or D to check your answer.
Explain why, when finding one moving object's velocity as measured by a second moving observer (with both velocities already known relative to the ground), you must subtract the two ground-frame velocities rather than add them. Illustrate with Car A (25 m/s east, ground frame) and Car B (15 m/s east, ground frame).
A train moves at a constant 20 m/s relative to the ground. A passenger drops a ball inside the train. Which statement correctly compares the acceleration measured by the passenger (train frame) with the acceleration measured by an observer on the ground?
Select A, B, C, or D to check your answer.
Using calculus, show why a puck's acceleration, as measured by a passenger inside a train moving at a constant velocity, equals the puck's acceleration as measured by an observer on the ground.
Now suppose the train itself is speeding up (accelerating) rather than moving at constant velocity, and the same ball is dropped inside it. Which statement is correct about what the train passenger and the ground observer will measure for the ball's acceleration?
Select A, B, C, or D to check your answer.
Explain, in terms of the boundary statement for this topic, why this course can generally assume every reference frame is inertial unless a problem states otherwise — and what would need to be added to the model if a frame were accelerating (non-inertial) instead.