Solved Examples of Finding Resultant Velocity using Vector Addition

📚 Quick Study Guide

🔍 Vector addition is used to find the resultant velocity when an object has multiple velocities acting on it. 💡 The resultant velocity is the single velocity that represents the combined effect of all individual velocities. 📝 Vectors can be added graphically using the head-to-tail method or parallelogram method. ➕ Mathematically, vectors are added by resolving them into their components (x and y) and then adding the components separately. 📐 The magnitude of the resultant vector can be found using the Pythagorean theorem: $R = \sqrt{Rx^2 + Ry^2}$. 🧭 The direction of the resultant vector can be found using trigonometry: $θ = tan^{-1}(\frac{Ry}{Rx})$. ✏️ Remember to pay attention to the direction (angle) of each vector. Choose a consistent coordinate system.

Practice Quiz

1. A boat is traveling east at 8 m/s across a river that flows south at 6 m/s. What is the magnitude of the resultant velocity of the boat?
   1. 2 m/s
   2. 10 m/s
   3. 14 m/s
   4. 48 m/s
2. An airplane is flying north at 200 m/s while encountering a wind blowing east at 50 m/s. What is the direction of the airplane's resultant velocity (relative to north)?
   1. 14° east of north
   2. 76° east of north
   3. 14° north of east
   4. 76° north of east
3. A cyclist rides east at 12 m/s and then turns and rides north at 9 m/s. What is the magnitude of the cyclist's resultant velocity?
   1. 3 m/s
   2. 15 m/s
   3. 21 m/s
   4. 108 m/s
4. A bird flies with a velocity of 10 m/s at an angle of 30° north of east. What is the eastward component of the bird's velocity?
   1. 5 m/s
   2. 8.66 m/s
   3. 10 m/s
   4. 11.55 m/s
5. A car is moving at 25 m/s, and a passenger walks towards the front of the car at 2 m/s. What is the resultant velocity of the passenger relative to the ground?
   1. 2 m/s
   2. 23 m/s
   3. 25 m/s
   4. 27 m/s
6. A swimmer can swim at 1.5 m/s in still water. They swim directly across a river that flows at 0.8 m/s. What is the swimmer's resultant speed?
   1. 0.7 m/s
   2. 1.3 m/s
   3. 1.7 m/s
   4. 2.3 m/s
7. A ball is thrown upward with a velocity of 15 m/s from a train moving horizontally at 20 m/s. What is the horizontal component of the ball's initial velocity relative to the ground?
   1. 0 m/s
   2. 15 m/s
   3. 20 m/s
   4. 35 m/s