Class 11 >> Physics >> kinematics >> relative-velocity >> solve-boat-and-river-problems
Skip to Practice

solve-boat-and-river-problems

🚀 Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. In relative velocity problems, we analyze the motion of objects in relation to each other, particularly in scenarios involving rivers and boats. When a boat moves in a river, its velocity relative to the ground is affected by the velocity of the river current. Understanding how to calculate relative velocities is crucial for solving problems involving boats crossing rivers or moving upstream and downstream.

Theory Explanation

Understanding Relative Velocity

Relative velocity is the velocity of one object as observed from another object. When dealing with a boat in a river, we consider the velocity of the boat relative to the water and the velocity of the water relative to the ground. The relative velocity of the boat with respect to the ground can be calculated by vector addition of the boat's velocity and the river's velocity.

\[ v_{bg} = v_{bw} + v_{wg} \]

Key Points

  • 🎯 Relative velocity is the velocity of one object as observed from another object.
  • 🎯 When a boat moves in a river, its velocity relative to the ground is the vector sum of its velocity relative to the water and the velocity of the water.
  • 🎯 To cross a river directly, the boat must have a component of its velocity directed upstream to counteract the current.

🛠 Simulation is being generated. Please check back in a few moments.

Examples:💡

A boat can row at a speed of 5 m/s in still water. The river flows at a speed of 3 m/s. What is the speed of the boat relative to the ground when it is rowing directly across the river?

Solution:

Step 1: Identify the velocities: Boat's speed (v_bw) = 5 m/s, River's speed (v_wg) = 3 m/s.

Step 2: Since the boat is rowing directly across, we can use the Pythagorean theorem to find the resultant velocity: v_bg = √(v_bw^2 + v_wg^2).

\[ v_{bg} = \sqrt{5^2 + 3^2} = \sqrt{34} \approx 5.83 m/s. \]

Step 3: Thus, the speed of the boat relative to the ground is approximately 5.83 m/s.

Common Mistakes

  • Mistake: Students often forget to consider the direction of the river's current when calculating the boat's velocity relative to the ground.

    Correction: Always draw a vector diagram to visualize the directions of the boat's velocity and the river's current.

  • Mistake: Confusing the speeds when calculating the resultant velocity, especially when using the Pythagorean theorem.

    Correction: Ensure to correctly identify which speeds are perpendicular and apply the theorem only in those cases.

← Back Start Practice