2d and 3d motion
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This chapter discusses motion in two and three dimensions, including projectile motion, uniform circular motion, and relative motion. It provides important equations of motion for topics like constant acceleration, position and velocity in 3D, projectile motion, ball dropping, kicking a football at an angle, and solving problems involving objects thrown off cliffs or dropped from planes. Sample problems are provided for topics like determining maximum height, velocity, time, and distance of a kicked football or supplies dropped from a rescue plane.
2d and 3d motion
- 1. Chapter 3 Motion in Two or Three Dimensions
- 2. Which ship gets hit first?
- 3. Chapter 3 Kinematics in Two or Three Dimensions: Position in 3D, velocity in 3D, acceleration in 3D Projectile Motion Uniform Circular Motion Relative Motion
- 4. Chapter 3
- 5. Important Equations of Motion Motion in uniform acceleration 𝒗 = 𝒗 𝟎 + 𝒂𝒕 𝒙 = 𝒙 𝟎 + 𝒗 𝟎 𝒕 + 𝟏 𝟐 𝒂𝒕 𝟐
- 6. Position in 3 dimensions
- 7. Velocity in 3 dimensions
- 10. X and Y motion are separable
- 11. Equations of motion under constant acceleration
- 12. Firing up in the air at an angle
- 13. Kick a football A football is kicked at angle θ0 with respect to the ground with speed v0. we can calculate: The maximum height The velocity at the maximum height The time of travel before the football hits the ground How far it hits the ground What angle maximizes the distance traveled Assume the ball leaves the foot at ground level and ignore air resistance
- 14. Rock and Cliff Problem A ball is thrown horizontally out off a cliff of a height h above the ground. The ball hits the ground a distance D from the base of the cliff. Assuming the ball was moving horizontally at the top and ignoring air friction, what was its initial velocity?
- 15. Rescue Plane You are the pilot of a rescue plane. Your mission is to drop supplies to isolated mountain climbers on a rocky ridge a height h below. If your plane is traveling horizontally with a speed of VO: How far in advance of the recipients (horizontal distance) must the goods be dropped?
- 16. Rescue Plane cont. b) Suppose instead, that your plane can’t get to that position. Instead you must release the supplies a horizontal distance D in advance of the mountain climbers. What vertical velocity should you give the supplies so that they arrive precisely at the climbers position. c) What is the speed of the supplies as they hit the ground?
- 17. Football Punt A football is kicked at angle θ0 with a velocity v0. the ball leaves the punters foot h meters above the ground. How far does it travel, in the x-direction, before it hits the ground?
- 20. Uniform Circular Motion A string is in a horizontal circle above her head. If the string breaks at the instant shown, which arrow best represents the path the rock will follow?