Dr. Loveless Curiosity Lab

Rowing and Running

Student investigator: Arjav

A person rows across a river and then runs along the shore. Rowing and running have different speeds, so the shortest path may not be the fastest path.

Choose the speeds, drag the landing point to make your guess, and then hit play to compare your choice to the optimal route.

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Choose Your Landing Spot

First choose a rowing speed and a running speed. Then drag the landing point on the right side of the river to choose where you think the fastest landing spot is. Hit play to see how close you were.

Rowing Speed —
Running Speed —
Your Landing Choice x = — km
Animation Time 0.00 hr
Rowing and Running Visual
Drag the landing point. The purple optimal path appears when the animation passes \(T=0.5\).

Where It Started

Arjav started with a Math 124 optimization problem about rowing across a river and running along the shore. The original problem asks where to land so the total travel time is as small as possible.

The visual turns the formula into a story: one route has two pieces, and each piece has its own speed.

Going Further

The next step is to add a second graph showing total time as a function of the landing point. Then students can see their chosen route in the picture and the corresponding point on the time graph.

This also connects naturally to shortest-time paths, Snell’s Law, and optimization in physics.

Further Reading