Question

This question is directly related to this lab. There is a river in front of you that flows due South at 3.0m/s. You launch a toy boat across the river with the front of the boat pointed due East. When you tested the boat on a still pond, the boat moved at 4.0m/s. Now as it moves to the opposite bank, it travels at some speed relative to you, sitting in your chair. What is this speed? Express your answer in m/s but do not type the units. Two significant digits will be enough.

Answer 1

The river is flowing due south and we can take south as the x direction of the cartesian coordinate and the boat is moving towards east. We can consider the east direction as y direction of the cartesian coordinate. Now the relative speed of the boat with respect to the observer is the resultant velocity of the boat and the river.

The velocity of the boat in still water V_b = 4 m/s and the velocity of the river V_r = 3 m/s. The river is flowing in the x direction and the boat is moving in the y direction. So the angle between their velocity vector is 90^0.

Therefore the resultant velocity of the boat is

V = (V_b² + V_r² + V_bV_rcos90)^1/2

V = (4² + 3² + 3*4*0)^1/2

V = 5.00 m/s. This is the relative velocity of boat with respect to the observer.