RELATIVE AND ABSOLUTE MOTION NUMERICAL PROBLEMS

QUESTION:

A boat is moving downstream on a river. The river flows at a speed of 3 m/s relative to the riverbank. The boat’s engine propels it at a speed of 7 m/s relative to the water.

1) Determine the speed of the boat relative to the riverbank (absolute motion).

2) If the boat turns around and starts moving upstream, what will be its speed relative to the riverbank?

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Solution:

1. Downstream Motion (Absolute Motion):

When the boat is moving downstream, its speed relative to the riverbank is the sum of its speed relative to the water and the speed of the river flow.

Let \( v_{b/r} \) be the speed of the boat relative to the riverbank, \( v_{b/w} \) be the speed of the boat relative to the water, and \( v_{r} \) be the speed of the river.

Given:

• \( v_{b/w} = 7 \, \text{m/s} \)
• \( v_{r} = 3 \, \text{m/s} \)

The absolute speed of the boat downstream is:

\( v_{b/r} = v_{b/w} + v_{r} = 7 + 3 = 10 \, \text{m/s} \)

So, the speed of the boat relative to the riverbank when moving downstream is 10 m/s.

2. Upstream Motion (Absolute Motion):

When the boat moves upstream, its speed relative to the riverbank is the difference between its speed relative to the water and the speed of the river flow.

The absolute speed of the boat upstream is:

\( v_{b/r} = v_{b/w} – v_{r} = 7 – 3 = 4 \, \text{m/s} \)

So, the speed of the boat relative to the riverbank when moving upstream is 4 m/s.