Ann is driving a motorboat across a river that is 2 km wide at 20 km/h in still water, with a 5 km/h river current. To calculate how far downstream and how long it will take Ann to cross the river, the solution breaks down Ann's movement into perpendicular components: traveling perpendicular to the current at 20 km/h will take 6 minutes to cross the width, and in that time the current will carry her 500 meters downstream, so she will land 500 meters downstream from the dock in 6 minutes.
How far downstream will Ann land crossing a river in a motorboat
1. Any ideas on how to do this?
Ann is driving a motorboat across a river that is 2 km wide. The boat has a speed of 20 km/h in
still water, and the current in the river is flowing at 5 km/h. Ann heads out from one bank of the
river for a dock directly across from her on the opposite hank. She drives the boat in direction
perpendicular to the current. How far downstream from the dock will Ann land? How long will
it take Ann to cross the river!
Solution
Think in terms of perpendcular components
First perpendicular to direction of flow
time taken = 2km/20kmph =0.1 hr = 6 min
( Width/ speed along )
in this time = 5*0.1 = 0.5 km = 500 m travelled in direction along river
