1. A boat can be rowed at Think & Prepare 1. In all the questions below, think about motion from the point of view of an observer on the boat and the point of view of an observer on the shore. BW = 8.5 km/h in still water. WS (a) How much time is required to row 1.2 km downstream (East) in a river moving ✓ws = 3.8 km/h relative to the shore? Time required to row 1.2 downstream = 6.1 (b) How much time is required for the return trip? Time for the return trip = 13.85 min Direction of boat = 22.85° (c) In what direction must the boat be aimed to row straight across the river? Express the angle in degrees measured West of North. Vws VBW West of North. min 0 VBS (d) Suppose the river is 1.2 km wide. What is the velocity of the boat with respect to shore and how much time is required to get to the opposite shore?
1. A boat can be rowed at Think & Prepare 1. In all the questions below, think about motion from the point of view of an observer on the boat and the point of view of an observer on the shore. BW = 8.5 km/h in still water. WS (a) How much time is required to row 1.2 km downstream (East) in a river moving ✓ws = 3.8 km/h relative to the shore? Time required to row 1.2 downstream = 6.1 (b) How much time is required for the return trip? Time for the return trip = 13.85 min Direction of boat = 22.85° (c) In what direction must the boat be aimed to row straight across the river? Express the angle in degrees measured West of North. Vws VBW West of North. min 0 VBS (d) Suppose the river is 1.2 km wide. What is the velocity of the boat with respect to shore and how much time is required to get to the opposite shore?
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![**1. A boat can be rowed at \( \vec{v}_{BW} = 8.5 \, \text{km/h} \) in still water.**
**Think & Prepare**
1. In all the questions below, think about motion from the point of view of an observer on the boat and the point of view of an observer on the shore.
(a) How much time is required to row 1.2 km downstream (East) in a river moving \( \vec{v}_{WS} = 3.8 \, \text{km/h} \) relative to the shore?
Time required to row 1.2 km downstream = \(\cancel{6.1} \checkmark\) min
(b) How much time is required for the return trip?
Time for the return trip = \(\cancel{13.85} \checkmark\) min
(c) In what direction must the boat be aimed to row straight across the river? Express the angle in degrees measured West of North.
![Diagram showing vectors \( \vec{v}_{WS} \), \( \vec{v}_{BW} \), and \( \vec{v}_{BS} \)]
- Diagram explanation: The diagram shows a triangle formed by the vectors. \( \vec{v}_{BW} \) is the velocity of the boat in still water pointing to the left (West), \( \vec{v}_{WS} \) is the velocity of the water pointing upwards (North), and \( \vec{v}_{BS} \) is the resultant velocity of the boat with respect to the shore. The angle θ is between \( \vec{v}_{BW} \) and \( \vec{v}_{BS} \).
Direction of boat = \(\cancel{22.85°} \checkmark\) West of North.
(d) Suppose the river is 1.2 km wide. What is the velocity of the boat with respect to shore and how much time is required to get to the opposite shore?
\(\vec{v}_{BS} = \cancel{7.83} \checkmark \, \text{km/hr}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2Fca62b95b-95a1-470e-900d-56aa1859d548%2F26f3z_processed.png&w=3840&q=75)
Transcribed Image Text:**1. A boat can be rowed at \( \vec{v}_{BW} = 8.5 \, \text{km/h} \) in still water.**
**Think & Prepare**
1. In all the questions below, think about motion from the point of view of an observer on the boat and the point of view of an observer on the shore.
(a) How much time is required to row 1.2 km downstream (East) in a river moving \( \vec{v}_{WS} = 3.8 \, \text{km/h} \) relative to the shore?
Time required to row 1.2 km downstream = \(\cancel{6.1} \checkmark\) min
(b) How much time is required for the return trip?
Time for the return trip = \(\cancel{13.85} \checkmark\) min
(c) In what direction must the boat be aimed to row straight across the river? Express the angle in degrees measured West of North.
![Diagram showing vectors \( \vec{v}_{WS} \), \( \vec{v}_{BW} \), and \( \vec{v}_{BS} \)]
- Diagram explanation: The diagram shows a triangle formed by the vectors. \( \vec{v}_{BW} \) is the velocity of the boat in still water pointing to the left (West), \( \vec{v}_{WS} \) is the velocity of the water pointing upwards (North), and \( \vec{v}_{BS} \) is the resultant velocity of the boat with respect to the shore. The angle θ is between \( \vec{v}_{BW} \) and \( \vec{v}_{BS} \).
Direction of boat = \(\cancel{22.85°} \checkmark\) West of North.
(d) Suppose the river is 1.2 km wide. What is the velocity of the boat with respect to shore and how much time is required to get to the opposite shore?
\(\vec{v}_{BS} = \cancel{7.83} \checkmark \, \text{km/hr}\)
Transcribed Image Text:### Velocity and Time Calculation for Crossing a River
#### (d) Scenario 1: Boat Velocity with Respect to Shore
- **River Width**: 1.2 km
- **Velocity of Boat with Respect to Shore (\( \vec{V}_{BS} \))**: 7.83 km/hr
- **Time Required to Reach the Opposite Shore**: 5.36 minutes
#### (e) Scenario 2: Boat Aiming Straight Across the River
- **Velocity Diagram Explanation**:
- The diagram is a vector triangle illustrating the relationship between different velocities:
- \( \vec{V}_{BW} \) (boat with respect to water)
- \( \vec{V}_{WS} \) (water with respect to shore)
- \( \vec{V}_{BS} \) (boat with respect to shore)
- An angle \( \theta \) is formed between \( \vec{V}_{BW} \) and the riverbank direction, indicating the component of velocities.
- **Time Required to Cross Straight**: 4.94 minutes
- **Distance Downstream**: 0.272 km
This analysis demonstrates how aiming strategies affect both crossing time and downstream drift when navigating a river.
Expert Solution
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We are given the velocity of the stream. We are also given the velocity of boat in still water. Motion is a relative term. The velocities we incur are relative to observer which is observing the motion.
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