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Understanding Projectile Motion in 2D: Basics and Formulas

Learn about projectile motion, including horizontal and vertical components, formulas, and problem-solving strategies in this comprehensive guide from January 4, 2017.

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Understanding Projectile Motion in 2D: Basics and Formulas

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  1. Motion in Two-Dimensions Projectile Motion Notes January 4, 2017

  2. Projectile Motion • A projectile can be anything that moves through the air after it has been given an initial “thrust” or input force • Projectiles are only under one force as they move through the air –GRAVITY! • We ignore air resistance in most cases to simply the problems • There are two general categories: • Projectiles launched horizontally • Projectiles launched at an angle

  3. Important Facts about Projectile Motion: • Vertical and horizontal motions are independent of each other. • We can relate the height, time in the air, and initial vertical velocity of the projectile by using its vertical motion, then determine the range (x-distance) • We use basic motion equations to solve!

  4. Look at the pictures:

  5. Horizontal Projectile Motion Demonstrations:

  6. Horizontal and Vertical Components of Motion: Vertical Motion ONLY! Horizontal Motion ONLY! Vertical and Horizontal Motion!

  7. Horizontal and Vertical Components: • The path of the projectile is known as the TRAJECTORY! • Dxwill stand for displacement on the x-axis or in the horizontal direction. This is also known as the range! • Dywill stand for displacement on the y-axis or in the vertical direction. This is also known as the height! • vxwill stand for velocity in the horizontal direction. • vywill stand for velocity the vertical direction.

  8. Horizontal and Vertical Components: Starting Point of the Projectile Motion

  9. Horizontal and Vertical Components: x will be positive y will be positive vx will be positive vy will be positive

  10. Horizontal and Vertical Components: x will be positive y will be positive vx will be positive vy will be positive x will be positive y will be negative vx will be positive vy will be negative

  11. Horizontal and Vertical Components: x will be positive y will be positive vx will be positive vy will be positive x will be positive y will be negative vx will be positive vy will be negative x will be negative y will be negative vx will be negative vy will be negative

  12. Horizontal and Vertical Components: x will be negative y will be positive vx will be negative vy will be positive x will be positive y will be positive vx will be positive vy will be positive x will be positive y will be negative vx will be positive vy will be negative x will be negative y will be negative vx will be negative vy will be negative

  13. TIME WILL ALWAYS BE POSITIVE!

  14. What about the acceleration due to GRAVITY?(The reason for the “sign” will become clear as we do examples!) - 9.81 m/s2 - 9.81 m/s2 - 9.81 m/s2 - 9.81 m/s2

  15. Projectile Motion Basic Formulas: • Dx = vxi t • Dy = vyit + ½ at2 • Where: • Dx is horizontal displacement • Dy is vertical displacement • vxi is horizontal initial velocity • vyi is vertical initial velocity • t is the time in flight • a is the acceleration, usually gravity!

  16. This is Splat the Cat R.I.P Splat the Cat’s days are numbered….Why??

  17. Projectiles Launched Horizontally • Splat the cat is tossed horizontally at 20 m/s • off a cliff that is 50 m high. • How long is the Splat in the air? • b) How far (THE RANGE) from the base of the cliff does Splat land?

  18. Problems Solving Strategy • 1. Write known and unknown variables • 2. Write variables for x and y directions • 3. Find TIME first! What’s missing? ay = g = -9.81m/s2 y = 0 vyi = 0 ax = 0 vxi = 20 m/s t = ? y = -50 m x= ? x= 0

  19. Your Turn: • A plane that is moving 200 m/s drops a package. The package falls -1102.5 meters to the ground. • Draw a picture and label ALL of the components! • How long was the package in the air? • How far down range (Dx) did the package hit the ground?

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