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?
I converted the miles per hour into meters per second and the mile stretch into meters but cannot figure out the answer.
To calculate how far downstream the captain will be from the target when she lands on the east bank, we need to consider the effect of the river's current on the ferryboat's motion.
Let's start by converting the speed of the boat from miles per hour (mph) to meters per second (m/s):
15.0 mph = 15.0 * 0.44704 m/s = 6.7056 m/s
Next, let's convert the distance of the stretch from miles to meters:
1.29 miles = 1.29 * 1609.34 meters ≈ 2074.88 meters
Now that we have the speed of the boat in m/s and the distance of the stretch in meters, we can calculate the time it will take for the boat to cross the river:
Time = Distance / Speed = 2074.88 meters / 6.7056 m/s ≈ 309.65 seconds
During this time, the river's current will move the boat downstream.
The downstream distance can be calculated using the equation:
Downstream Distance = Time * River's Speed
Downstream Distance = 309.65 seconds * 2.58 m/s ≈ 798.90 meters
Therefore, the captain will be approximately 798.90 meters downstream from the target when she lands on the east bank of the river.
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.
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.