Question

You row a boat perpendicular to the shore of a river that flows at 3.0 m/s. The velocity of your boat is 4.0 m/s relative to the water. What is its velocity relative to the shore? What is the compound of your velocity perpendicular to the shore?

Answer 1

To determine the velocity of the boat relative to the shore, we need to consider the vector addition of the boat's velocity relative to the water and the velocity of the river.

1. Velocity of the boat relative to the shore: Let's assume the boat is moving horizontally across the river. The velocity of the boat relative to the shore can be found by adding the velocity of the boat relative to the water and the velocity of the river.

   Given: Velocity of the boat relative to the water (v_boat) = 4.0 m/s Velocity of the river (v_river) = 3.0 m/s (flowing perpendicular to the shore)

   The velocity of the boat relative to the shore (v_shore) can be found by vector addition: v_shore = v_boat + v_river

   v_shore = 4.0 m/s + 3.0 m/s v_shore = 7.0 m/s

   Therefore, the velocity of the boat relative to the shore is 7.0 m/s.

2. Compound of the boat's velocity perpendicular to the shore: The compound of the boat's velocity perpendicular to the shore can be determined by subtracting the velocity of the river from the boat's velocity relative to the water.

   The compound velocity (v_compound) can be calculated as: v_compound = v_boat - v_river

   v_compound = 4.0 m/s - 3.0 m/s v_compound = 1.0 m/s

   Therefore, the compound of the boat's velocity perpendicular to the shore is 1.0 m/s.