A river is flowing due south at 3m/s. A motorboat has a maximum velocity of 6m/s in still water. Calculate the relative velocity of the boat with respect to the riverbank if:

Question

1) the boat is moving downstream
2)the boat is moving upstream

Answer 1

To calculate the relative velocity of the motorboat with respect to the riverbank, we can consider the velocities in vector form.

Given:

• Velocity of the river (\( V_{river} \)): 3 m/s (south)
• Maximum velocity of the boat in still water (\( V_{boat} \)): 6 m/s

1) When the boat is moving downstream

When the boat moves downstream, its velocity is in the same direction as the river's flow. Therefore, the velocities add up.

\[ V_{relative, downstream} = V_{boat} + V_{river} \]

Substituting the known values:

\[ V_{relative, downstream} = 6 , \text{m/s} + 3 , \text{m/s} = 9 , \text{m/s} \]

2) When the boat is moving upstream

When the boat moves upstream, its velocity is in the opposite direction to the river's flow. Therefore, the river's velocity is subtracted from the boat's velocity.

\[ V_{relative, upstream} = V_{boat} - V_{river} \]

Substituting the known values:

\[ V_{relative, upstream} = 6 , \text{m/s} - 3 , \text{m/s} = 3 , \text{m/s} \]

Summary of Results

1. Relative velocity when moving downstream: \( 9 , \text{m/s} \) (south)
2. Relative velocity when moving upstream: \( 3 , \text{m/s} \) (north)