To solve this problem, we need to break it down into the horizontal and vertical components.
First, let's convert the speed of the ferryboat from miles per hour to meters per second.
Given:
Speed of the ferryboat in still water = 15.0 mph
Speed of the river = 2.58 m/s
We convert the speed of the ferryboat to meters per second:
1 mile = 1609.34 meters
1 hour = 3600 seconds
15.0 mph * (1609.34 meters / 1 mile) * (1 hour / 3600 seconds) = 6.71 m/s
Now we have the speed of the ferryboat in still water, which is 6.71 m/s.
Next, we need to find the time it takes for the ferryboat to cross the river.
Distance = Speed × Time
Time = Distance / Speed
Distance = 1.29 miles = 1.29 miles * 1609.34 meters / 1 mile = 2072.21 meters
Time = 2072.21 meters / 6.71 m/s = 308.71 seconds
Now we know that it takes 308.71 seconds for the ferryboat to cross the river.
During this time, the river is pushing the ferryboat downstream.
The distance the ferryboat moves downstream can be calculated using the formula:
Distance downstream = Speed of river × Time
Distance downstream = 2.58 m/s × 308.71 seconds = 796.32 meters
Therefore, when the ferryboat lands on the east bank, it will be approximately 796.32 meters downstream from the target location.