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Understanding Relative Velocity: Crossing a River and Airplane Navigation

This chapter explores the concept of relative velocity in two dimensions through practical examples involving a boat crossing a river and an airplane flying in the wind. We analyze a boat moving perpendicularly across a river with specific velocities and determine both its velocity relative to the shore and the time taken to cross. Additionally, we discuss how wind affects an airplane's trajectory, including adjustments pilots make to ensure correct ground speed and heading despite crosswinds. This insightful examination provides a clearer understanding of relative motion in real-world scenarios.

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Understanding Relative Velocity: Crossing a River and Airplane Navigation

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  1. Kinematics in Two Dimensions Chapter 3

  2. 3.4 Relative Velocity

  3. 3.4 Relative Velocity Example 11 Crossing a River The engine of a boat drives it across a river that is 1800m wide. The velocity of the boat relative to the water is 4.0m/s directed perpendicular to the current. The velocity of the water relative to the shore is 2.0m/s. (a) What is the velocity of the boat relative to the shore? (b) How long does it take for the boat to cross the river?

  4. Plane in the Wind To determine the resulting velocity - add the velocity of the airplane to the velocity of the air. Resulting Velocity = Velocity of object wrt the air + velocity of air wrt the ground VPG = VPA +VAG

  5. What if the wind is blowing towards the north? The resulting velocity of the airplane is relative to the ground.

  6. What if the wind is blowing towards the West? The resulting velocity of the airplane is relative to the ground.

  7. What if the plane is flying towards the Southeast and wind is to the West? The resulting velocity of the airplane is relative to the ground.

  8. Suppose he needs to fly south and the wind was blowing to the west? The resulting velocity of the airplane relative to the ground must be south! But what angle to fly at?

  9. Heading Øo 100 km/h R Ø = -75.5o 25 km/h The pilot would have to fly his plane in a direction of -75.5o to compensate for the wind.

  10. Resulting Velocity? Øo 100 km/h R R = 96.8 km/h 25 km/h This velocity is relative to the ground and is sometimes called the ground speed.

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