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Projectile Motion

Explore the concepts of projectile motion and resultant vectors, including examples and equations. Learn about the factors affecting projectile motion and how to calculate horizontal and vertical components of velocity. Includes practical applications and a lab activity.

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Projectile Motion

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  1. Projectile Motion

  2. The resultant of two perpendicular vectors is the diagonal of a rectangle constructed with the two vectors as sides.

  3. The velocity of something is often the result of combining two or more other velocities. • If a small airplane is flying north at 80 km/h relative to the surrounding air and a tailwind blows north at a velocity of 20 km/h, the plane travels 100 kilometers in one hour relative to the ground below. • What if the plane flies into the wind rather than with the wind? The velocity vectors are now in opposite directions. The resulting speed of the airplane is 60 km/h.

  4. THINK! • Suppose that an airplane normally flying at 80 km/h encounters wind at a right angle to its forward motion—a crosswind. Will the airplane fly faster or slower than 80 km/h?

  5. Now consider an 80-km/h airplane flying north caught in a strong crosswind of 60 km/h blowing from west to east.

  6. A ball’s velocity can be resolved into horizontal and vertical components.

  7. Projectile Motion • Projectile– any object that is projected by some means and continues in motion. • Follows a parabolic path • Two-dimensional motion of an object • Vertical • Horizontal

  8. Types of Projectile Motion • Horizontal • Motion of a ball rolling freely along a level surface • Horizontal velocity is ALWAYS constant • Vertical • Motion of a freely falling object • Force due to gravity • Vertical component of velocity changes with time • Parabolic • Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

  9. Examples of Projectile Motion • Launching a Cannon ball

  10. think! At the instant a horizontally pointed cannon is fired, a cannonball held at the cannon’s side is released and drops to the ground. Which cannonball strikes the ground first, the one fired from the cannon or the one dropped? Answer:Both cannonballs fall the same vertical distance with the same acceleration g and therefore strike the ground at the same time.

  11. Equations • X- Component • Y- Component • Vectors Note: g= 9.8 m/s^2

  12. Factors Affecting Projectile Motion • What two factors would affect projectile motion? • Angle • Initial velocity Initial Velocity Angle

  13. The velocity of a projectile is shown at various points along its path. Notice that the vertical component changes while the horizontal component does not. Air resistance is neglected.

  14. The velocity of a projectile is shown at various points along its path. Notice that the vertical component changes while the horizontal component does not. Air resistance is neglected.

  15. The velocity of a projectile is shown at various points along its path. Notice that the vertical component changes while the horizontal component does not. Air resistance is neglected.

  16. The velocity of a projectile is shown at various points along its path. Notice that the vertical component changes while the horizontal component does not. Air resistance is neglected.

  17. The velocity of a projectile is shown at various points along its path. Notice that the vertical component changes while the horizontal component does not. Air resistance is neglected.

  18. The paths of projectiles launched at the same speed but at different angles. Neglect air resistance. What do you notice?

  19. Maximum range is attained when the ball is batted at an angle of nearly 45°.

  20. Consistency • Without air resistance, a projectile will reach maximum height in the same time it takes to fall from that height to the ground. • The deceleration due to gravity going up is the same as the acceleration due to gravity coming down. • The projectile hits the ground with the same speed it had when it was projected upward from the ground.

  21. think! A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? Its horizontal acceleration? Answer:Its vertical acceleration is g because the force of gravity is downward. Its horizontal acceleration is zero because no horizontal force acts on it.

  22. Sin – Cos – Tan • SOH CAH TOA

  23. Class Exercise An object is fired from the ground at 100m/s at an angle of 30 degrees with the horizontal • Calculate the horizontal and vertical components of the initial velocity • After 2.0 seconds, how far has the object traveled in the horizontal direction? • How high is the object at this point?

  24. Solution • Part a • Part b • Part c

  25. Applications Any Ideas?

  26. LAB TIME!!!

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