A small boat is crossing a lake on a windy day. During some interval of time, the boat undergoes the given displacement Ar. AF = (3.19 m)i + (2.91 m)j During the same interval of time, the wind exerts the given constant force F on the boat. F = (253 N)î - (109 N)Ĵ What is the total work done on the boat by the wind over this period of time? work: What is the angle between the direction of the wind force and the direction of the boat's motion during this time interval? angle:
A small boat is crossing a lake on a windy day. During some interval of time, the boat undergoes the given displacement Ar. AF = (3.19 m)i + (2.91 m)j During the same interval of time, the wind exerts the given constant force F on the boat. F = (253 N)î - (109 N)Ĵ What is the total work done on the boat by the wind over this period of time? work: What is the angle between the direction of the wind force and the direction of the boat's motion during this time interval? angle:
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![Title: Calculating Work and Angle in Boat Dynamics
**Scenario**:
A small boat is crossing a lake on a windy day. During a given time interval, the boat undergoes a displacement \(\Delta \vec{r}\).
**Displacement**:
\[
\Delta \vec{r} = (3.19 \, \text{m}) \hat{\imath} + (2.91 \, \text{m}) \hat{\jmath}
\]
**Force Exerted by Wind**:
During the same time interval, the wind exerts a constant force \(\vec{F}\) on the boat.
\[
\vec{F} = (253 \, \text{N}) \hat{\imath} - (109 \, \text{N}) \hat{\jmath}
\]
**Task 1: Total Work Done**
Calculate the total work done on the boat by the wind over this period of time.
\[
\text{Work:} \quad \underline{\hspace{5cm}} \, \text{J}
\]
**Task 2: Angle Between Wind Force and Boat Motion**
Determine the angle between the direction of the wind force and the direction of the boat's motion during this time interval.
\[
\text{Angle:} \quad \underline{\hspace{5cm}} \, \text{degrees}
\]
**Note**: The transcription does not include any graphs or diagrams but focuses on mathematical expressions and problem-solving in physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9081bc6b-9817-477c-9b8d-7c2dcc8c93d8%2Ff0781c7a-b55f-4bfd-b283-bd05feea62e5%2Fyusr21_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Calculating Work and Angle in Boat Dynamics
**Scenario**:
A small boat is crossing a lake on a windy day. During a given time interval, the boat undergoes a displacement \(\Delta \vec{r}\).
**Displacement**:
\[
\Delta \vec{r} = (3.19 \, \text{m}) \hat{\imath} + (2.91 \, \text{m}) \hat{\jmath}
\]
**Force Exerted by Wind**:
During the same time interval, the wind exerts a constant force \(\vec{F}\) on the boat.
\[
\vec{F} = (253 \, \text{N}) \hat{\imath} - (109 \, \text{N}) \hat{\jmath}
\]
**Task 1: Total Work Done**
Calculate the total work done on the boat by the wind over this period of time.
\[
\text{Work:} \quad \underline{\hspace{5cm}} \, \text{J}
\]
**Task 2: Angle Between Wind Force and Boat Motion**
Determine the angle between the direction of the wind force and the direction of the boat's motion during this time interval.
\[
\text{Angle:} \quad \underline{\hspace{5cm}} \, \text{degrees}
\]
**Note**: The transcription does not include any graphs or diagrams but focuses on mathematical expressions and problem-solving in physics.
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