Question

Suppose at one point along the Nile River a ferryboat must travel straight across a 1.01-mile stretch from west to east. At this location, the river flows from south to north with a speed of 2.04 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?

Answer 1

`494.3` m

Step-by-step explanation:

Consider the motion of the boat across the stretch from west to east direction :

`v_(b)` = velocity of boat = 15 mph

`L` = length of the stretch = 1.01 miles

`t` = Time taken to reach the opposite end

Time taken to reach the opposite end is given as

`t = (L)/(v_(b))`

`t = (1.01)/(15)`

`t =0.0673` h

`t = (0.0673) (3600)` sec (Since 1 h = 3600 sec)

`t = 242.3` sec

`v_(r)` = speed of river = 2.04 m/s

`d` = distance traveled downstream

Distance traveled downstream is given as

`d = v_(r) t`

`d = (2.04) (242.3)`

`d = 494.3` m