How to Use the Relative Motion Simulator
 

Choosing a Scenario

• Pick Train for 1D relative motion along a line. Pick Riverboat for 2D relative motion, where a boat crosses a river with a current.
  Note for teachers: Start students on Train. Once they can say what each person would measure, the riverboat is the same idea with vectors.
   

Train: Building Your Scenario

• Under Elements, choose which objects to include: the Train, Person 1, Person 2, and a Ball. Person 1 can stand on the ground or ride on the train. The Ball needs Person 1, because it is rolled by Person 1.

• Use the Velocities sliders to set each speed in m/s. Train speed (v_T) and Person 2 speed (v_P2) are measured in the ground frame. When Person 1 is on the train, their slider changes to Person 1 / train (v_P1T), which is their speed relative to the train. The Ball slider is the Ball's speed relative to Person 1 (v_B).

• Use Initial Positions to set where each object starts, and Animation speed to slow the motion down or speed it up.

• Press Play to run the scenario, Pause to stop it, and Reset to return to the start.
   

Train: Reference Frame

• Choose who is "standing still" with the Reference Frame buttons: Ground, Train, Person 1, Person 2, or Ball. Only the objects in your scenario appear.

• The velocity of every object on the canvas is shown relative to the frame you pick, so the reference object always shows a velocity of 0. Everything else changes by the same amount, so two objects' velocity relative to each other never changes. Switching frames does not change your slider settings, which stay at their original values.

• Check the Summary panel, which lists each object's speed "In [frame] frame" and also shows the ground-frame values v_P1/gnd and v_B/gnd.
  Mastery tip: Predict first. Before you switch frames, calculate what each object's velocity should be by subtracting the reference object's velocity from it. Then switch and check your answer against the canvas arrows and the Summary.
  Note for teachers: Try two people walking toward each other at equal speeds. In the ground frame both arrows are equal and opposite. In either person's frame, that person stops and the other approaches at double the speed. Students often expect the stopped person to keep their arrow.
   

Train: Display

• Show velocity vectors draws an arrow for each object, labeled v_T, v_P1, v_P2, and v_B with their values.

• Show coordinates adds the x-axis and labels the positions, and the timer t shows the elapsed time.

• Use the eye icon on the canvas to hide or show the vectors quickly, and the fullscreen icon to give the canvas more room.
   

Riverboat: Parameters

• Boat heading (θ) sets the direction the boat points. 0° is straight across, positive angles point upstream, and negative angles point downstream.

• Boat speed (v_b) is how fast the boat moves relative to the water.

• Current speed (v_c) is how fast the water moves relative to the bank. Negative values flow left and positive values flow right.

• River width and Animation speed set the size of the river and how quickly the motion plays.

• Trajectory preview draws a dotted line showing the path the boat will take before you launch.

• Press Launch to send the boat across, and use the reset icon to start over. Launch is disabled when the heading has no crossing component.
   

Riverboat: Reading the Results

• The Summary panel shows the Heading (θ), Resultant speed, Crossing time, Angle from normal, Lateral drift, and Landing x (far bank).

• Show velocity vectors draws the arrows v_b, v_c, and v_r (the resultant). Show vector diagram adds an inset that shows the three vectors tip to tail. Show coordinates adds the grid and axes.

• The boat's actual motion is the vector sum of its velocity in the water and the water's velocity.
  Mastery tip: Predict the crossing time before you press Launch. Only the part of the boat's velocity that points across the river sets the crossing time, so the current changes where the boat lands but not how long the trip takes.
  Note for teachers: Have students find the heading that makes the boat land straight across. It is a good introduction to why a boat must aim upstream to compensate for the current.
   

Riverboat: Challenge Mode

• Check Enable target practice to place a target on the far bank. Set its position with Target x-offset, or press Randomise target for a new one.

• Choose a heading and launch. The canvas shows ✓ HIT! or ✗ MISS when the boat lands. Click the canvas to reset and try again.

• While target practice is on, the Summary panel and the trajectory preview are hidden, so students have to calculate the answer instead of reading it.
  Mastery tip: Work out the angle and landing point on paper first, then launch to test your answer.