To sketch the velocity and displacement vector diagrams for the given scenario, follow these steps:

1. Draw a horizontal line to represent the stream. Label the direction of the stream as "West".

2. Draw a vector arrow pointing to the left (West) to represent the velocity of the stream. Label this vector as "15.0 m/s".

3. Draw a vertical line to represent the path of the boat. Label this direction as "South".

4. Draw a vector arrow pointing downwards (South) to represent the velocity of the boat in still water. Label this vector as "20.0 m/s".

5. The displacement of the boat is the resultant of the boat's velocity and the stream's velocity. To find this, draw a vector from the tail of the boat's velocity vector to the head of the stream's velocity vector. This vector represents the actual path of the boat.

6. The length of the displacement vector can be calculated using the Pythagorean theorem (since the boat's velocity and the stream's velocity are perpendicular to each other). The displacement is sqrt((20.0 m/s)^2 + (15.0 m/s)^2) = 25.0 m/s.

7. The width of the stream is given as 60 m. This can be represented as a horizontal line on the displacement vector diagram.

8. The time it takes for the boat to cross the stream can be calculated by dividing the width of the stream by the component of the boat's velocity that is perpendicular to the stream (which is the boat's velocity in still water). The time is 60 m / 20.0 m/s = 3.0 s.

9. The distance downstream that the boat ends up can be calculated by multiplying the time it takes to cross the stream by the velocity of the stream. The distance is 3.0 s * 15.0 m/s = 45 m. This can be represented as a vertical line on the displacement vector diagram.

Remember, the direction of the vectors is very important in this diagram. The boat's velocity vector should be pointing South, the stream's velocity vector should be pointing West, and the displacement vector should be pointing in the direction that the boat actually travels (which is South-West in this case).

Question

To sketch the velocity and displacement vector diagrams for the given scenario, follow these steps:

1. Draw a horizontal line to represent the stream. Label the direction of the stream as "West".

2. Draw a vector arrow pointing to the left (West) to represent the velocity of the stream. Label this vector as "15.0 m/s".

3. Draw a vertical line to represent the path of the boat. Label this direction as "South".

4. Draw a vector arrow pointing downwards (South) to represent the velocity of the boat in still water. Label this vector as "20.0 m/s".

5. The displacement of the boat is the resultant of the boat's velocity and the stream's velocity. To find this, draw a vector from the tail of the boat's velocity vector to the head of the stream's velocity vector. This vector represents the actual path of the boat.

6. The length of the displacement vector can be calculated using the Pythagorean theorem (since the boat's velocity and the stream's velocity are perpendicular to each other). The displacement is sqrt((20.0 m/s)^2 + (15.0 m/s)^2) = 25.0 m/s.

7. The width of the stream is given as 60 m. This can be represented as a horizontal line on the displacement vector diagram.

8. The time it takes for the boat to cross the stream can be calculated by dividing the width of the stream by the component of the boat's velocity that is perpendicular to the stream (which is the boat's velocity in still water). The time is 60 m / 20.0 m/s = 3.0 s.

9. The distance downstream that the boat ends up can be calculated by multiplying the time it takes to cross the stream by the velocity of the stream. The distance is 3.0 s * 15.0 m/s = 45 m. This can be represented as a vertical line on the displacement vector diagram.

Remember, the direction of the vectors is very important in this diagram. The boat's velocity vector should be pointing South, the stream's velocity vector should be pointing West, and the displacement vector should be pointing in the direction that the boat actually travels (which is South-West in this case).

Knowee AI · Accepted Answer