**Problem Description:**Johnny comes across a river that is 252 meters wide. He sees that the water flows eastward with a uniform velocity of 1.10 m/s. Johnny sees his friend Sarah start her boat at point A on the south bank and start to cross the river to point B which is on the other side. Suppose the trip takes 3 minutes. Figure out the velocity of Sarah's boat with respect toa) Johnny who is stationary on the ground b) A floating goose that's moving with the water.**Diagram Explanation:**Below the problem description is a graphical representation of the scenario:1. **River Flow:** The diagram shows the river flowing eastward (to the right) with a velocity (\(v_{river}\)) of 1.1 m/s.2. **Distance:** The river width (north-south direction) is marked as 252 meters.3. **Points:** Point A is situated on the south bank, where Sarah starts her boat. Point B is directly north of Point A on the opposite bank.4. **Boat's Path:** Sarah is crossing directly from Point A to Point B.**Steps to Solve:**1. **Calculate the Time of Crossing:** The boat trip takes 3 minutes. Converting minutes to seconds: \[ 3 \text{ minutes} = 3 \times 60 = 180 \text{ seconds} \]2. **Calculate Sarah's Boat Velocity Across the River:** The northward velocity component, which is perpendicular to the flow of the river, is: \[ v_{north} = \frac{252 \text{ m}}{180 \text{ s}} = 1.4 \text{ m/s} \]3. **Velocity with Respect to Johnny:** Johnny observes both the eastward river flow and the northward motion of Sarah's boat. Using vector components: \[ v_{east} = 1.1 \text{ m/s} \quad \text{(velocity of river)} \] \[ v_{north} = 1.4 \text{ m/s} \quad \text{(Sarah's boat velocity across)} \] The resultant velocity (\(v_{res}\)) can be calculated using the Pythagorean theorem: \[ v_{res} = \sqrt{v

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Description: **Problem Description:**Johnny comes across a river that is 252 meters wide. He sees that the water flows eastward with a uniform velocity of 1.10 m/s. Johnny sees his friend Sarah start her boat at point A on the south bank and start to cross the r

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hnny comes across a river that is 252 meters wide. He sees at the water flows eastward with a uniform velocity of 10m/s. Johnny sees his friend Sarah start her boat at point A the south bank and start to cross the river to point B which on the other side. Suppose the trip takes 3 minutes. Figure t the velocity of sarah's boat with respect to a) Johnny who is stationary on the ground b) A floating goose that's moving with the water. N B VE S Vriver = 1.1 m/s A 252 m

hnny comes across a river that is 252 meters wide. He sees at the water flows eastward with a uniform velocity of 10m/s. Johnny sees his friend Sarah start her boat at point A the south bank and start to cross the river to point B which on the other side. Suppose the trip takes 3 minutes. Figure t the velocity of sarah's boat with respect to a) Johnny who is stationary on the ground b) A floating goose that's moving with the water. N B VE S Vriver = 1.1 m/s A 252 m

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**Problem Description:**

Johnny comes across a river that is 252 meters wide. He sees that the water flows eastward with a uniform velocity of 1.10 m/s. Johnny sees his friend Sarah start her boat at point A on the south bank and start to cross the river to point B which is on the other side. Suppose the trip takes 3 minutes. Figure out the velocity of Sarah's boat with respect to

a) Johnny who is stationary on the ground
b) A floating goose that's moving with the water.

**Diagram Explanation:**

Below the problem description is a graphical representation of the scenario:

1. **River Flow:** The diagram shows the river flowing eastward (to the right) with a velocity (\(v_{river}\)) of 1.1 m/s.
2. **Distance:** The river width (north-south direction) is marked as 252 meters.
3. **Points:** Point A is situated on the south bank, where Sarah starts her boat. Point B is directly north of Point A on the opposite bank.
4. **Boat's Path:** Sarah is crossing directly from Point A to Point B.

**Steps to Solve:**

1. **Calculate the Time of Crossing:**
The boat trip takes 3 minutes. Converting minutes to seconds:
\[
3 \text{ minutes} = 3 \times 60 = 180 \text{ seconds}
\]

2. **Calculate Sarah's Boat Velocity Across the River:**
The northward velocity component, which is perpendicular to the flow of the river, is:
\[
v_{north} = \frac{252 \text{ m}}{180 \text{ s}} = 1.4 \text{ m/s}
\]

3. **Velocity with Respect to Johnny:**
Johnny observes both the eastward river flow and the northward motion of Sarah's boat. Using vector components:
\[
v_{east} = 1.1 \text{ m/s} \quad \text{(velocity of river)}
\]
\[
v_{north} = 1.4 \text{ m/s} \quad \text{(Sarah's boat velocity across)}
\]
The resultant velocity (\(v_{res}\)) can be calculated using the Pythagorean theorem:
\[
v_{res} = \sqrt{v

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