# Solve 2D Vectors Problem: Ferry Boat Crosses River

• jen333
In summary, the group discusses a 2D problem involving a ferry boat crossing a river with a current. Through the use of diagrams and vector notation, they find the distance the boat drifts during the crossing. They then explore the impact of the boat's velocity on its final landing point.
jen333
Hey everyone,
i have a question here on 2D problems that I'm pretty much stuck on

A ferry boat has a speed of 9.0km/h in calm water. Its pilot takes it on a heading due north across a river that has a current of 4.0km/h west. It takes 15 minutes to cross the river.
a) how far downstream does the ferry land? (the answer is 1.0km)

for a, (i've drawn a diagram) I've found the width of the river which is 2.3km and I've also found the velocity of the boat relative to the shore which is 9.8 km/h, 24 degrees W of N. from there, I'm stuck.

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You don't need the widht of the river. All you need to know is that he was crossing for 15 minutes, and that the current was 4km west.

This is enough to find out how far he drifted during the cross.

oooo...hehehe, i feel sort of silly after just calculating that.
thank you.
but i have one more question, just wondering: why doesn't the boat's 9.0km/h affect how far the boat lands? wouldn't that impact the angle in which the boat is going across the river along with the 4.0km/h?
i hope you understand what I'm trying to say...

The ferryman maintains a strictly northward heading.

Thus, his velocity North will compound with but will not affect his velocity West. The velocities are at 90 degrees to one another. You see?

Think of it this way. West is the direction down the x-axis (left, and into the negative numbers), while North is the direction up the y-axis.
This allows us to use vector notation.

$$\vec v = [-4.0 \frac{km}{h}, 9.00 \frac{km}{h}]$$

The x and y components (or i and j, as they're often called) are separate.

Last edited by a moderator:
YES! totally makes sense to me
Thx for the help!
jen

## 1. How do I find the resultant vector when a ferry boat crosses a river?

To find the resultant vector when a ferry boat crosses a river, you need to use the Pythagorean theorem and trigonometric functions. First, draw a diagram of the situation, with the river representing the horizontal component and the boat's velocity representing the vertical component. Then, use the Pythagorean theorem to find the magnitude of the resultant vector, and trigonometric functions to find its direction.

## 2. What is the difference between a 2D vector and a 1D vector?

A 2D vector has two components, typically represented as x and y, while a 1D vector only has one component, typically represented as x or y. This means that a 2D vector has both magnitude and direction, while a 1D vector only has magnitude.

## 3. How do I determine the direction of the ferry boat's velocity in a 2D vector problem?

The direction of the ferry boat's velocity can be determined by using the inverse trigonometric function tangent (tan). Take the ratio of the vertical component (representing the boat's velocity) to the horizontal component (representing the river's velocity), and use the inverse tan function to find the angle of the resultant vector.

## 4. Can a ferry boat's velocity change while it crosses a river?

Yes, a ferry boat's velocity can change while it crosses a river. This can happen if there are external forces acting on the boat, such as wind or currents, or if the boat changes its own velocity, such as by using its engines.

## 5. How do I account for the ferry boat's speed and direction in a 2D vector problem?

To account for the ferry boat's speed and direction in a 2D vector problem, you need to break down its velocity into its horizontal and vertical components. The horizontal component will represent the river's velocity, and the vertical component will represent the boat's velocity. You can then use these components to find the resultant vector using the Pythagorean theorem and trigonometric functions.

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