Projectile Motion

1. Projectile Motion

2. Vocabulary • Resultant • Component • Resolution • Projectile • Trajectory -The path that the projectile follows • Range – pg 77

3. What is a PROJECTILE? • An object that is projected (launched) • It continues in motion due to its own inertia, • Is only acted upon by gravity • No force in the x-direction, only in the y-direction (gravity) • Gravity ALWAYS acts in the y-direction, and ONLY the y-direction

4. So Projectile Motion… • Describes the motion of an object in TWO dimensions • We will only consider projectiles that stay close to Earth (so ag = -9.8 m/s2) • We will continue to disregard air resistance

5. Some Vocabulary… • PROJECTILE • The object being launched/thrown/projected • TRAJECTORY • The path that the projectile follows • RANGE • The horizontal displacement of the projectile • MAXIMUM HEIGHT • The vertical displacement of the projectile at the top of its flight

6. The Components of Projectile Motion • We ALWAYS break projectile motion down into its x- and y-components • INITIAL VELOCITY: vi • Use trigonometry to find vix and viy • vix = vicosθ • viy = visinθ • ACCELERATION: a • ay = -9.8 m/s2 • ax = 0 m/s2 • Why? Think gravity and Newton’s 1st Law… vi viy vix

7. Remember Freefall??? • Recall that… • a = -9.8 m/s2, regardless if the object is moving up or moving down • The ONLY force acting on the object is GRAVITY • Projectile Motion has the same conditions, and moves in the x-direction simultaneously.

8. What does this look like? • For horizontally projected objects: • For objects projected at an angle:

9. VERY IMPORTANT!!! • The components act INDEPENDENTLY of one another!!! • When we combine the x- and y-components, we get the characteristic parabola-shape • Vx remains constant (a = 0) • Vy changes because of gravity (a = -9.8 m/s2)

10. How do I determine the direction? • If an object is projected at an angle, the direction is measured from the rightward horizontal

11. To Calculate Projectile Motion… • We use the kinematic equations • Remember… Δd = vit + ½ at2 • RANGE (x-displacement) uses x-components and total time • Δdx = vixttotal + ½ axttotal2 = vixttotal • Remember that a = 0 in the x-direction • HEIGHT (y-displacement) uses y-components • Δdy = viyt + ½ ayt2 • Remember that a = -9.8 m/s2 in the y-direction

12. More on Calculations • ay = (vfy2 – viy2) / 2Δdy • (to find max height) • ay = (vfy – viy) / t • (to find time to max height) • These only apply in the y-direction (vx doesn’t change) • ay = -9.8 m/s2 ALWAYS • Remember, at the top of its path, a projectile’s vy = 0 (so vfy = 0)

13. EXAMPLES • A cannonball is fired from a cannon at an angle of 32° and an initial velocity of 54 m/s. • What are the components of the initial velocity? • How long does it take the cannonball to reach maximum height? • What is the cannonball’s maximum height? • What is the total time of travel? • What is the cannonball’s range?

14. A cannonball is fired from a cannon at an angle of 32 ° and an initial velocity of 54 m/s. A. What are the components of the initial velocity?

15. A cannonball is fired from a cannon at an angle of 32 ° and an initial velocity of 54 m/s. B. How long to maximum height?

16. A cannonball is fired from a cannon at an angle of 32 ° and an initial velocity of 54 m/s. C. What is the maximum height?

17. A cannonball is fired from a cannon at an angle of 32 ° and an initial velocity of 54 m/s. D. What is the total time?

18. A cannonball is fired from a cannon at an angle of 32 ° and an initial velocity of 54 m/s. E. What is the range?