To find the boat's speed relative to the riverbank, we can use the concept of vector addition. The boat's velocity with respect to the riverbank is the vector sum of the boat's velocity with respect to the water and the water's velocity with respect to the riverbank.
Given:
- Boat's velocity with respect to water = 5 m/s
- Water's velocity with respect to riverbank = 4 m/s
To calculate the boat's velocity with respect to the riverbank, we can use the Pythagorean theorem because the boat's velocity with respect to the riverbank and the water's velocity with respect to the riverbank form a right triangle.
Using the Pythagorean theorem: Boat's velocity with respect to riverbank = √((Boat's velocity with respect to water)^2 + (Water's velocity with respect to riverbank)^2) Boat's velocity with respect to riverbank = √((5^2) + (4^2)) Boat's velocity with respect to riverbank = √(25 + 16) Boat's velocity with respect to riverbank = √41 Boat's velocity with respect to riverbank ≈ 6.4 m/s
Therefore, the boat's speed relative to the riverbank is approximately 6.4 m/s.
