IB Physics River Crossing Problems
/A tutorial sheet of harder questions on this topic follows and will be added to. A reference is Physics Education Vol 34 Number 3 May 1999, p 148
- A boat leaves point P on one side of a river bank and travels with a constant speed u relative to the water in a direction toward Q on the other side of the river directly opposite P and distant d from it. If r is the distance of the boat from Q and the angle between r and PQ is 𝜽, show that r = dsec𝜽/(sec𝜽+tan𝜽)u/v, where v is the speed of the river.
In question 1 if u = v show that the path is an arc of a parabola.
A boat crosses a river of width w with velocity of constant magnitude u always aimed toward a point on the opposite shore directly opposite its starting point. If the water flows at a constant speed u how far downstream does the boat arrive on the opposite shore? [w/2]
