The Relative Velocity of the Boat with Respect to Water:

To determine the relative velocity of the boat with respect to the water, we need to consider the velocities of both the boat and the water with respect to the ground.

Given Information:
- Velocity of the boat with respect to the ground: 3i + 4j
- Velocity of the water with respect to the ground: -3i - 4j

Relative Velocity:
The relative velocity of the boat with respect to the water can be calculated by subtracting the velocity of the water from the velocity of the boat.

Relative velocity of the boat with respect to the water = Velocity of the boat - Velocity of the water

= (3i + 4j) - (-3i - 4j)

Simplifying the equation, we get:

= 3i + 4j + 3i + 4j

= 6i + 8j

Hence, the relative velocity of the boat with respect to the water is 6i + 8j.

Explanation:

- The velocity of an object is a vector quantity that describes its speed and direction of motion. It can be represented as a vector in terms of its components along the x-axis (i) and y-axis (j).
- In this case, the velocity of the boat with respect to the ground is given as 3i + 4j. This means that the boat is moving with a speed of 3 units in the positive x-direction and 4 units in the positive y-direction.
- Similarly, the velocity of the water with respect to the ground is given as -3i - 4j. This means that the water is moving with a speed of 3 units in the negative x-direction and 4 units in the negative y-direction.
- To determine the relative velocity of the boat with respect to the water, we subtract the velocity of the water from the velocity of the boat.
- The resulting relative velocity is 6i + 8j, which means that the boat is moving with a speed of 6 units in the positive x-direction and 8 units in the positive y-direction with respect to the water.
- The relative velocity of the boat with respect to the water is important in situations where the boat needs to navigate through a current or determine its actual speed and direction of motion in the water.