Gravity and free fall Revisited Objectives Define the

Gravity and free fall Revisited

Objectives • Define the conditions for free fall. • Describe and analyze the motion of objects in free fall using the equations for constant acceleration.

What is free fall? An object is in free fall whenever it moves solely under the influence of gravity, regardless of its direction. A ball falling down, with negligible air resistance A ball thrown up, with negligible air resistance A ball launched at ANY angle, as long as there is negligible air resistance

Gravity and free fall Near Earth’s surface, free-falling objects have a downward acceleration of 9. 8 m/s 2. If an object is dropped from rest, then. . . • after 1 second its velocity is -9. 8 m/s. • after 2 seconds its velocity is -19. 6 m/s. • after 3 seconds its velocity is __? ___ • after 10 seconds its velocity is __? ___

Gravity and free fall Near Earth’s surface, free-falling objects have a downward acceleration of 9. 8 m/s 2. If an object is dropped from rest, then. . . • after 1 second its velocity is -9. 8 m/s. • after 2 seconds its velocity is -19. 6 m/s. • after 3 seconds its velocity is -29. 4 m/s. • after 10 seconds its velocity is -98 m/s.

Describe free fall with equations The free fall equations are identical to the equations for motion with constant acceleration: The only difference is that you already know the acceleration because it is always 9. 8 m/s 2 downward.

Gravity and free fall If an object is dropped from rest then. . . • after 1 second its velocity is -9. 8 m/s. • after 2 seconds its velocity is -19. 6 m/s. • after 3 seconds its velocity is -29. 4 m/s. • after 4 seconds its velocity is -39. 2 m/s. . . and so on. . REALLY? Do falling objects REALLY keep moving faster and faster?

Solving free fall problems 1) Define your coordinate system: • If you decide up is positive, g = -9. 8 m/s 2 • If you decide down is positive, g = +9. 8 m/s 2 2) Write the equations of motion, substituting g for a. 1) Eliminate any terms that are zero. 2) Work out a solution strategy.

Example free fall problem From what height should you drop a ball if you want it to hit the ground in exactly 1. 0 second? Asked: x Given: t v 0 Relationship: Solution:

Example free fall problem From what height should you drop a ball if you want it to hit the ground in exactly 1. 0 second? Asked: x Given: t = 1. 0 s, g = -9. 8 m/s 2 (assume v 0 = 0 m/s and x 0 = 0 m) Relationship: Solution:

Example free fall problem From what height should you drop a ball if you want it to hit the ground in exactly 1. 0 second? Asked: x Given: t = 1. 0 s, g = -9. 8 m/s 2 (assume v 0 = 0 m/s and x 0 = 0 m) Relationship: Solution: The negative sign means that the final position is 4. 9 m below the initial position. 4. 9 m high

Bullets Fired vs. Dropped A bullet is dropped from a height of 2 meters. How long does it take to hit the ground?

Bullets Fired vs. Dropped A bullet is dropped from a height of 2 meters. How long does it take to hit the ground? Given: the height, which is x. Unknown: t Equation:

Bullets Fired vs. Dropped A bullet is fired horizontally from a gun at a velocity of 400 m/s and from a height of 2 meters. • How long does it take to hit the ground? • How far does it travel?

Bullets Fired vs. Dropped A bullet is fired horizontally from a gun at a velocity of 400 m/s and from a height of 2 meters. • How long does it take to hit the ground? The same amount of time as it did if it were dropped! • How far does it travel? Good question! How can we figure this out?

Range of a projectile If you know how long a projectile has been in the air and how fast it has been fired, then you can figure out how far it moves down the range!

Range of a projectile If you know how long a projectile has been in the air and how fast it has been fired, then you can figure out how far it moves down the range! But how? Remember—we know it’s speed in the x direction and the amount of time it’s been in the air.

Objects launched horizontally follow two different sets of rules. In the x direction they move at a CONSTANT SPEED. In the y direction, they move with CONSTANT ACCELERATION—just like a freely falling object.

Equations for projectile motion With x 0 = 0 and ax = 0, the With y 0 = 0 and ay = -g, the x-axis equations are: y-axis equations are: Notice that vx is constant. The projectile never speeds up or slows down in the x direction! These are just the equations for motion with constant acceleration, with a = g.

Projectile motion How do you use these equations to solve problems? Let’s look at an example. 30 m/s

Projectile motion A projectile is fired horizontally off the top of a cliff with an initial velocity of 30 m/s. It hits the ground 2. 0 seconds later. a) What is the initial velocity in the x direction? in the y direction? 30 m/s

Projectile motion A projectile is fired horizontally off the top of a cliff with an initial velocity of 30 m/s. It hits the ground 2. 0 seconds later. a) What is the initial velocity in the x direction? in the y direction? vx = 30 m/s vy 0 = 0 m/s 30 m/s

Projectile motion A projectile is fired horizontally off the top of a cliff with an initial velocity of 30 m/s. It hits the ground 2. 0 seconds later. b) How far from the base of the cliff does the projectile land? What variable are you being asked for? 30 m/s

Projectile motion A projectile is fired horizontally off the top of a cliff with an initial velocity of 30 m/s. It hits the ground 2. 0 seconds later. b) How far from the base of the cliff does the projectile land? 30 m/s You are being asked for x. 60 m

Projectile motion A projectile is fired horizontally off the top of a cliff with an initial velocity of 30 m/s. It hits the ground 2. 0 seconds later. c) How high is the cliff? What variable are you being asked for? 30 m/s

Projectile motion A projectile is fired horizontally off the top of a cliff with an initial velocity of 30 m/s. It hits the ground 2. 0 seconds later. c) How high is the cliff? You are being asked for y. 30 m/s The projectile falls 19. 6 m, so the cliff is 19. 6 m high.