Suppose at one point along the Nile River a ferryboat must travel straight across a 1.29-mile stretch from west to east. At this location, the river flows from south to north with a speed of 2.58 m/s. The ferryboat has a motor that can move the boat forward at a constant speed of 15.0 mph in still water. If the captain points the boat directly at the target location on the east bank of the river, how far downstream will she be from the target when she lands on the east bank?

Question

I converted the miles per hour into meters per second and the mile stretch into meters but cannot figure out the answer.

Answer 1

This is a vector problem. You are adding two velocities at 90 degrees.

distance across 1.29miles
distance north=2.58m/s*timeinwater

time across: 1.29/speedofboat
now I notice the 1.29 is in miles, the 15 in miles /hour. Convert all to meters per second. Solve for time across.

finally, far downstream=distance North.