2. Gravity Free falling bodies undergo a constant acceleration. This constant downward acceleration is gravity. Earth’s gravity = (g) = - 9.81 m/s²

3. Gravity (cont.) When an object is moving at a downward velocity, it is moving in the direction of gravitational acceleration. 1 TON (-) g CRASH (-) v

4. More Gravity When an object is moving at an upward velocity, it is moving in the opposite direction of gravitational acceleration. (-) g (+) v

5. Question What will fall faster when released at the same height and at the same time…………a text book or a pencil???

6. Even More Gravity The rate at which an object falls is independent of its mass.

7. Sample Problem #1 A robot probe drops a camera off the rim of a 239 m high cliff on Mars where the free-fall acceleration is -3.70 m/s². a. a. What is the velocity of the camera when it hits the ground? b. b. How long does it take for the camera to hit the ground?

8. a. Find v f ! Δ y = - 239 m a = -3.70 m/s²v i = 0.00 m/s v f ² = v i ² + 2aΔy v f ² = 2aΔy v f = √2aΔy v f = √2(-3.70 m/s² )(-239 m ) v f = 42.1 m/s down

9. b. Find Δt ! V f = V i + a(Δt) Δt = V f / a v f = - 42.1 m/s a = -3.70 m/s²v i = 0.00 m/s Δ y = - 239 m Δt = - 42.1 m/s / -3.70 m/s² Δt = 11.4 s

10. Sample Problem #2 Jason hits a volleyball so that it moves with an initial velocity of 6.00 m/s straight upward. If the ball starts from 2.00 m above the floor, how long will it be in the air before it strikes the floor?

11. 2.00 m V i = 6.00 m/s V f = 0.00 m/s a = -9.81 m/s² Step 1: Find out how high the ball reaches. V f ² = V i ² + 2aΔy Δy = (V f ²- V i ²) 2a Δy = -(6.00 m/s)² 2(-9.81 m/s²) Δy = -36.0 m²/s² -19.6 m/s² Δy= 1.84 m y tot = 1.84m + 2.00m = 3.84 m

12. Step 2: Find out the time of the ball traveling up! V f = 0.00 m/s V i = 6.00 m/s g = -9.81 m/s² V f = V i + a(Δt) Δt = (V f – V i ) / a Δt = – 6.00 m/s / -9.81 m/s² Δt up = 0.612 s

13. Step 3: Find time traveling down. Δy = -3.84 m g = - 9.81 m/s² V i = 0.00 m/s Δy = V i (Δt) + ½(a)(Δt)² 0.885 s = Δt down Δt = √(2Δy)/a Δt = √2( -3.84 m) /-9.81 m/s²

14. Step 4: Solve for the total time of ball before it hits the floor. Total time = Δt up + Δt down Total time = 0.612 s + 0.885 s Total time = 1.50 s