A ferry boat is crossing a river that is 8.5 x 10^2 m wide.

In summary, the ferry boat crosses a river in 4.9 m/s S relative to the water and it takes 6.2 m/s to cross.
  • #1
Ayushi
2
0

Homework Statement


A ferry boat is crossing a river that is 8.5 x 10^2 m wide.

The average velocity of the water relative to the shore is 3.8 m/s E and the average velocity of the boat relative to the water is 4.9 m/s S.
How long does it take for the boat to get across?

Homework Equations

The Attempt at a Solution


The velocity of the boat relative to the shore is 6.2 m/s [52° E of S].
 
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  • #2
Hello ayushi, :welcome:
Ayushi said:
The velocity of the boat relative to the shore is 6.2 m/s [52° E of S].
How did you come to that conclusion ?
 
  • #3
BvU said:
Hello ayushi, :welcome:

How did you come to that conclusion ?
I used the pythagorean theorem to figure the velocity of the boat relative to the shore.
3.8 m/s E ^2 + 4.9 m/s S ^2
And got 6.2 m/s E of S
 
  • #4
Think of it from the point of view of the boat. How fast is the shore approaching if the boat is pointed straight across the river?

You'll also need the distance to the other shore, which I assume you were given even though you didn't include it.
 
  • #5
Ayushi said:
I used the pythagorean theorem to figure the velocity of the boat relative to the shore.
3.8 m/s E ^2 + 4.9 m/s S ^2
And got 6.2 m/s E of S
6.2 meters per second yes. But the angle is suspect.
RPinPA said:
You'll also need the distance to the other shore, which I assume you were given even though you didn't include it.
It is stashed in the title -- 850 meters.
 
  • #6
The problem statement does not specifically indicate whether the ferry is to land directly opposite its starting point, or just reach the other shore in the quickest time possible (although this is a common enough problem type that it is almost surely the former case). Just thought I'd point that out. Imprecisely stated problem statements can sometimes be time wasting as helpers have to tease out the details before being able to work the actual problem.
 
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Likes Merlin3189 and BvU

1. What is the distance that the ferry boat has to travel across the river?

The river is 8.5 x 10^2 m wide, which means the distance the ferry boat has to travel across the river is 850 meters.

2. How long does it take for the ferry boat to cross the river?

The time it takes for the ferry boat to cross the river depends on various factors such as the speed of the boat, the direction and strength of the current, and any external factors like wind or weather. Without these variables, it is impossible to determine the exact time it takes for the ferry boat to cross the river.

3. Is the width of the river constant or does it change?

The width of the river can change over time due to natural factors such as erosion or man-made factors such as construction or dredging. However, the given measurement of 8.5 x 10^2 m is a constant value in this scenario.

4. How deep is the river the ferry boat is crossing?

The depth of the river can vary at different points, so it is impossible to determine the exact depth without more information. However, the depth of the river at the point where the ferry boat is crossing is not relevant to the given information.

5. What is the purpose of knowing the width of the river?

The width of the river is a crucial measurement for engineers and navigators to determine the best route for the ferry boat to take and to ensure the boat has enough space to maneuver safely. It is also important for calculating the time and distance of the journey and for any necessary construction or maintenance of the ferry or the river itself.

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