A boy wishes to row directly across a river but the current flows at 1.5m.s-1 east. He can row at 3m.s-1. Draw a labelled vector diagram
To draw a vector diagram representing the situation, we need to first draw a coordinate system. Let's assume that the river flows from west to east, so it would be represented by the x-axis.
1. Start by drawing a horizontal line to represent the river's current. Label it "1.5 m/s" to indicate the velocity of the current.
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River's Current (1.5 m/s)
2. Then draw an arrow starting from the origin, pointing towards the right to represent the boat's velocity. Label it "3 m/s" to indicate the boat's velocity.
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River's Current (1.5 m/s)
→
Boat's Velocity (3 m/s)
3. Now, draw another arrow from the end of the boat's velocity vector to represent the resultant velocity or the actual path of the boat. Label it "Boat's Resultant Velocity."
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River's Current (1.5 m/s)
→
Boat's Velocity (3 m/s)
↓
Boat's Resultant Velocity
4. Finally, draw a right-angled triangle using the boat's velocity and the current vectors. Label the vertical side as "y" and the horizontal side as "x" to represent the boat's displacement.
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River's Current (1.5 m/s)
→
Boat's Velocity (3 m/s)
↓
Boat's Resultant Velocity
↓
⬓
x
→
Boat's Velocity
⬓
y
Make sure to label the sides of the triangle, the vectors, and accurately indicate their directions to complete the vector diagram.
To draw a labelled vector diagram for this situation, follow these steps:
1. Start by drawing a horizontal line to represent the river. Label it as "River" or "River Current".
2. Choose a scale for your diagram. For example, you can decide that 1 cm on the diagram represents 1 m/s.
3. Draw an arrow pointing right (east) on the river line. Label this arrow as "Current" or "1.5 m/s".
4. Draw a diagonal arrow pointing from the left side to the right side of the river line, slightly upstream. Label this arrow as "Boat Speed" or "3 m/s".
5. Draw a dotted line connecting the head of the boat speed arrow to the current arrow. This dotted line represents the resultant velocity (the actual path the boat will take).
6. Finally, label this dotted line as "Resultant Velocity" or "Boat Path".
The vector diagram should resemble a right triangle, with the current arrow representing the horizontal leg, the boat speed arrow representing the diagonal leg, and the resultant velocity representing the hypotenuse of the triangle.