Relative Motion quiz with answers

📚 Quick Study Guide

• 🧭 Relative Motion: Describes the motion of an object with regard to some other moving object.
• ➕ Velocity Addition: If object A moves with velocity $\vec{v}_{A}$ relative to object B, and object B moves with velocity $\vec{v}_{B}$ relative to a stationary observer, then the velocity of A relative to the observer is $\vec{v}_{A} + \vec{v}_{B}$.
• ➖ Subtraction for Relative Velocity: To find the velocity of object A relative to object B, use $\vec{v}_{A/B} = \vec{v}_{A} - \vec{v}_{B}$.
• 📏 Frames of Reference: The perspective from which motion is observed. Crucial for understanding relative motion.
• 💡 Important Note: Always pay attention to the direction of the velocities. Use vector addition/subtraction accordingly.

🤔 Practice Quiz

1. A boat is traveling east at 8 m/s relative to the water. The water is flowing south at 3 m/s. What is the boat's velocity relative to the ground?
   1. 5 m/s at 37° south of east
   2. 11 m/s at 21° south of east
   3. $\sqrt{73}$ m/s at 20.6° south of east
   4. 5 m/s at 37° east of south
2. A train is moving north at 30 m/s. A person walks east across the train at 2 m/s. What is the person's speed relative to the ground?
   1. 28 m/s
   2. 32 m/s
   3. $\sqrt{904}$ m/s
   4. $\sqrt{896}$ m/s
3. Two cars are approaching an intersection. Car A is traveling east at 20 m/s, and Car B is traveling north at 30 m/s. What is the velocity of Car A relative to Car B?
   1. 50 m/s at 56.3° north of east
   2. 10 m/s at 56.3° south of west
   3. $\sqrt{1300}$ m/s at 56.3° south of east
   4. $\sqrt{1300}$ m/s at 56.3° east of north
4. A plane flies with an airspeed of 200 km/h. There is a wind blowing from the west at 50 km/h. In what direction must the plane head to fly directly north?
   1. 14.5° east of north
   2. 14.5° west of north
   3. 75.5° east of north
   4. 75.5° west of north
5. A ball is thrown upwards at 10 m/s from a train moving horizontally at 20 m/s. What is the initial velocity of the ball relative to a stationary observer on the ground?
   1. 20 m/s horizontally
   2. 10 m/s vertically
   3. $\sqrt{500}$ m/s at 26.6° above the horizontal
   4. 30 m/s at 60° above the horizontal
6. Two boats are moving parallel to each other in the same direction. Boat A is moving at 15 m/s and Boat B is moving at 10 m/s. What is the relative velocity of Boat A with respect to Boat B?
   1. 25 m/s
   2. 5 m/s
   3. -5 m/s
   4. 0 m/s
7. An object is dropped from a plane flying horizontally at a constant speed. Neglecting air resistance, what is the horizontal velocity of the object as it falls, relative to the plane?
   1. Increasing
   2. Decreasing
   3. Zero
   4. Constant and equal to the plane's velocity