Relative Velocity Examples in Everyday Life: Trains, Boats, and Airplanes

📚 Quick Study Guide

• 🚂 Relative Velocity: The velocity of an object as observed from a particular reference frame.
• 🧭 Reference Frame: The point of view from which motion is observed. Common examples are the ground, a moving train, or a flowing river.
• ➕ Formula (1D): If object A is moving with velocity $v_{A}$ and object B is moving with velocity $v_{B}$, the velocity of A relative to B is $v_{AB} = v_A - v_B$.
• 📐 Formula (2D): Use vector subtraction: $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$. This often involves breaking velocities into components and using the Pythagorean theorem.
• 🌬️ Wind Effects: In aviation, wind significantly affects relative velocity (airspeed vs. ground speed).
• 🌊 Current Effects: Similarly, water currents affect a boat's relative velocity.

🧪 Practice Quiz

1. A train is moving eastward at 20 m/s. A person walks towards the front of the train at 2 m/s. What is the person's velocity relative to the ground?
   1. 18 m/s eastward
   2. 22 m/s eastward
   3. 18 m/s westward
   4. 22 m/s westward
2. A boat is traveling north across a river at 5 m/s. The river current is flowing east at 2 m/s. What is the magnitude of the boat's velocity relative to the shore?
   1. 3 m/s
   2. 7 m/s
   3. $\sqrt{29}$ m/s
   4. $\sqrt{21}$ m/s
3. An airplane is flying north with an airspeed of 200 km/h. A wind is blowing from the west at 50 km/h. What is the airplane's ground speed (magnitude of velocity relative to the ground)?
   1. 150 km/h
   2. 250 km/h
   3. $\sqrt{42500}$ km/h
   4. $\sqrt{37500}$ km/h
4. Two trains are moving towards each other on parallel tracks. Train A is moving east at 30 m/s, and Train B is moving west at 25 m/s. What is the relative velocity of Train A as seen by a passenger on Train B?
   1. 5 m/s eastward
   2. 5 m/s westward
   3. 55 m/s eastward
   4. 55 m/s westward
5. A car is driving north at 25 m/s. A motorcycle passes it, moving north at 30 m/s. What is the velocity of the motorcycle relative to the car?
   1. 5 m/s north
   2. 5 m/s south
   3. 55 m/s north
   4. 55 m/s south
6. A boat aims to cross a river directly north at 4 m/s. The river flows east at 3 m/s. At what angle (relative to north) must the boat steer to travel directly north?
   1. 36.87 degrees west of north
   2. 36.87 degrees east of north
   3. 53.13 degrees west of north
   4. 53.13 degrees east of north
7. An airplane flies with an airspeed of 250 km/h due east. If there's a 70 km/h wind blowing from the north, what is the plane's resulting speed relative to the ground?
   1. 180 km/h
   2. 320 km/h
   3. $\approx 259.8$ km/h
   4. $\approx 259.6$ km/h