Free Fall Chapter 2 Section 3

Free Fall  Free Fall – An object in free fall falls at a constant acceleration towards the surface of a planet neglecting air resistance.

Free Fall Acceleration of Gravity  Free fall acceleration is denoted with the symbol “g”.  At the surface of Earth, the free fall acceleration is approximately 9.8 m/s² or about 32 ft/sec²  Acceleration of gravity is a constant and doesn’t change.

Relating Physics and The Coordinate Plane  When calculating problems with free fall, acceleration due to gravity is negative  -9.8m/s²  Using the ideas from a coordinate plane in math class, the motion of an object can be described.  To the right – positive  To the left – negative  Downward – negative  Upward – positive  This holds true for the objects displacement, velocity, and acceleration since they are all vectors.

Displacement  Designate an origin.  Usually where the object begins its free fall motion.  Describing displacement from the origin  Above Origin – Positive Displacement  Below Origin – Negative Displacement

Velocity  Objects Velocity in Free Fall  Upward motion – Positive Velocity  Downward motion – Negative Velocity

Acceleration  Acceleration is a constant and is caused by the gravity of Earth.  a = -9.8m/s²  Gravity is always pulling downward on an object, so acceleration due to gravity will always be downward.

What Goes Up Must Come Back Down  Objects that are given a positive velocity straight upward will have to come back down with a negative velocity.  Objects that are thrown upward are still being pulled by gravity and will slow down at a rate of -9.8m/s². Once the objects reaches 0m/s it will start to fall back to earth at a rate of -9.8m/s²

Objects Motion During Free Fall  An object thrown straight up will have a positive velocity and a negative acceleration.  Object is slowing down  An object falling towards the earth will have a negative velocity and a negative acceleration.  Object is speeding up

Motion of an Object in Free Fall: Velocity  If an object is thrown upward with a positive velocity, the velocity of the object when it reaches the point of which it was thrown from will be the same value, just negative.  Example: If I throw a ball upward with a velocity of 15m/s, I will catch it in my hand with a velocity of -15m/s when it comes back down. As long as the origin doesn’t change.

Motion of an Object in Free Fall: Time  If it takes an object just as long to go up as it does to come back down.  Example: If I throw an object upward and it takes 5 seconds to reach maximum height. It will take 5 seconds to come back down to its original position of where it was thrown.

Maximum Height  An object at maximum height will have a velocity of 0 m/s.  The acceleration will still be -9.8m/s² at maximum height.  Gravity doesn’t disappears!

Positive velocity since the ball is moving upward. Negative Velocity Since the ball is moving downward. When ball reaches maximum height, the velocity = 0 Acceleration is a constant and is always -9.8m/s 2 When the ball is below the line, or origin, the ball has negative displacement. When the ball is above the line, or origin, the ball has positive displacement.

Example Problem #1  A rock falls off a cliff that is 100 meters high.  What is the velocity of the rock when it reaches the ground below the cliff?  How long did it take the rock to reach the ground?

Example Problem #2 1. Bill stands behind the backstop which is 6 meters high and wants to throw a baseball over to his buddy on the other side. How hard (with what velocity) does Bill have to throw it in order for the ball just to make it over the backstop?

Example Problem #3  Joe and Mary are hiking and come by a cave that goes straight down. Joe wants to know how deep the cave goes. So he drops a large rock off the cliff and measures the time it takes to reach the bottom. He hears the rock hit the water below in the cave about 6.3 seconds later. How deep is the cliff?

Example Problem #4  An arrow is shot straight upward with a velocity of 150m/s.  How long did it take the object to reach maximum height?  How long did it take the object to reach the ground from where it was shot?  How high did the arrow go?  Graph d vs. t / v vs. t and a vs. t of the arrow.

Graphs for Problem #4 d vs. t v vs. ta vs. t