PAGE EDITORS:Jake Deuel, Tyler Martin, Matias Lirman, Alex McDowell, and Harrison Kaplan

Natland Note: (10/07/13)

  • Some FREE-FALL notes are not present, e.g the graphs of free-fall motion when an object is dropped from a tree, thrown upward, etc.
    • Also, the "situations when acceleration is negative" etc. are also cut off from one of the pictures.
    • also, the discussion of what the area beneath a graph can mean is missing!
  • include sample videos of projectile motion problems/concepts. Take a good one from google.
  • Making the short video teaching a concept/problem. Talk with me about this.
  • Also, mention the conceptual questions we do in class, and the ranking task numbers that we do.

Your WIKI page will be due Friday (10/4) and will include both Chapters 2 & 3.

Make sure ALL of you are posting on the website if you ALL want full credit for the LAB GRADE!


BIG Three Kinematic Equations:




Terminal Velocity: the maximum velocity reached by an object because the [[#|force]] of gravity is equivalent to the force of air resistance on the object.

As you jump out of the plane, your velocity rapidly increases until you reach the terminal velocity at 50 m/s. This means that no matter how much longer the distance he is free falling, his velocity will no longer increase and will remain at 50 m/s until the parachute is opened. Once the parachute is opened, you will rapidly decelerate until you reach your new terminal velocity of 8 m/s.

Mythbusters bust the myth that a penny falling from the top of the Empire State Building would kill someone on the ground!

external image mofall.gif

As you look at this chart, the first thing you want to notice is that the acceleration remains constant at 9.8 m/(sec2). The acceleration of all free falling objects in a [[#|vacuum]] (no air resistance) will be the force of gravity which is 9.8 m/(sec2). The second thing that must be noticed is that going down or towards the surface of the Earth is considered the positive direction in this scenario. If the positive direction were up, then the acceleration would be -9.8 m/(sec2).

external image U1L5e2.gif
The above image discusses why all objects fall with the same acceleration in free-fall!

Projectile Motion Notes



Physics Classroom Link
Clicking on this link and selecting one of the subjects in lesson 2 will take you to a page with an explanation of the subject and multiple practice problems.

Here is an animation showing the change in the velocity components over time. The x component remains the same throughout the entire motion, but the magnitude of the y component increases. For an object launched upward the y component would decrease until reaching the peak of its motion, then it would begin to increase.


Ground to Ground: The above image shows how the velocity vector and its components change throughout a projectile's path.


This image shows how the range varies with launch angle (with the same launch speed). Note how the max. range is achieved using a launch angle of 45 degrees and that complimentary launch angles travel the same horizontal displacement! Note: This is only for the special case of "ground to ground" (when the launch height and landing height are the same).

external image projectile.gif
external image projectile.gif

The above image shows how the velocity vector (and its components) change throughout the trajectory of a projectile.

projectile motion.png

The above image shows the velocity vs time graph for a ball thrown up in the air. The slope of the red line is constant and should be -9.8 for the acceleration of gravity.

Projectile motion 2.gif
The image shows an object that is accelerated upwards towards point C and then goes into projectile motion. Notice that the object continues to go upwards even after going into projectile motion. Also the point D is equal to A1 +A2 +A3 from the velocity vs time graph

Above is a cool GIF that provides a visual of how the skater's V0x will equal the Vx of the skateboard. This allows him to do a flip and land directly back on his skateboard instead of landing in the same spot and having the skateboard roll away. This is the same idea as shooting a bullet straight in the air off the back of a truck and having the bullet land directly back in the barrel of the gun. Just thought a cool visual would help the concept sink in better.

Here is another fun video of a demonstration done at MIT by famous physics professor Walter Lewin. It shows the independence of horizontal and vertical motion

Projectile Motion
Click to Run

This is a PHET, an interactive projectile motion simulation in which you can vary parameters such as angle, initial velocity, and even add air resistance to see how it affects the motion of the projectile. Click and check, check it out!


1-D motion
Practice Problem 1 (PP1): I throw a ball upward with a velocity of 8 m/s. How long until it comes back into my hand? Try to solve this problem using three different methods.

  • Answer for PP1: (one answer)

PP 2) While riding on an elevator descending with a constant speed of 3.0 m/s, you accidentally drop a book from under your arm. (a) How long does it take for the book to reach the elevator floor, 1.2 m below your arm? (b) What is the book's speed when it hits the elevator floor?

  • Answers for PP2:
    • (a) 0.495 s
    • (b) 7.85 m/s

PP 3) A ball, dropped from rest, covers three-quarters of the distance to the ground in the last second of its fall. (a) From what height was the ball dropped? (b) What was the total time of fall?

  • Answers for PP3:

PP 4) A seagull, ascending straight upward at 5.20 m/s, drops a shell when it is 12.5 m above the ground. (a) What is the magnitude and direction of the shell's acceleration just after it is released? (b) Find the maximum height above the ground reached by the shell. (c) How long does it take for the shell to return to a height of 12.5 m above the ground? (d) What is the speed of the shell at this time?

  • Answers to PP4:

Projectile Motion
PP 5) A hockey player hits a "slap shot" in practice at a horizontal distance of 15 m from the net (with no goalie present). The net is 1.2 m high, and the puck is initially hit at an angle of 5.0 degrees above the horizontal with a speed of 50 m/s. Does the puck make it into the net?

Answer to PP 5:
PP 6) A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 1.1 seconds after leaving the dock has a magnitude of 7 m. What is the car's speed at the instance it drives off the edge of the dock?

Answer to PP6:

PP 7) A soccer player kicks the ball toward a goal that is 16.8 m in front of him. The ball leaves his foot at a speed of 16.0 m/s and an angle of 28 degrees above the ground. Find the speed of the ball when the goalie catches it in front of the net.

Answer to PP7:

PP 8) Suppose the water at the top of Niagara Falls has a horizontal speed of 2.7 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 75 degree angle below the horizontal?

Answer to PP8:


The Question:

In the 2014 Super bowl, the dolphins are losing by 4 to the 49ers with 9 seconds on the clock. On the last play, Ryan Tannehill breaks out on a run to the end zone. Ryan Tannehill jumps and is 1m in the air and 4m from the end zone after Patrick Willis takes out his legs. Ryan Tannehill is flying through the air at an angle of 45 degrees above the horizontal at an initial velocity of 6 m/s. The call on the field is a touchdown, but the play is under review. Did the Dolphins win the super bowl? (Did he land more than 4 meters away?)

This video discusses the kinematics equations we learned in class during the past week and how to apply them. (Don't worry about equation number 2, the one without acceleration)
(Shows an astronaut dropping a feather and hammer on the moon, confirming that, in the absence of air resistance, the two objects would fall with the same acceleration) (3:42)
("Mythbusters - Penny Drop". The Mythbusters bust the penny falling from the top of the empire state building myth!)
"Kittinger parachutes from 102,800 ft"..that is almost 20 miles above the surface of the Earth.
(This is a good general review of projectile motion and how to make calculations with projectile motion graphs)
(this is a really good practice review problem comprehensive steps showing the answer)
(These are all of the kinematic free response questions that the AP test has asked in the past. The answers are online but you might have difficulty finding the answers to questions before 2000)
  • On August 16, 1960, Kittinger donned a pressurized suit and rode a helium balloon craft to a height of 102,800 feet--almost at the edge of Earth's atmosphere--and jumped.
  • In the late 1950's, the U.S. Air Force set out to prove that a human could survive a fall from the outer limits of Earth's atmosphere. Kittinger's Excelsior missions were designed to test whether a pilot or astronaut could parachute to safety after an emergency bail-out from a damaged craft at high altitude.
  • Because the atmosphere was so thin, Kittinger said he felt no wind resistance and heard no sound during the first four minutes and 36 seconds of his fall toward Earth. "I had no visual reference on anything, so I thought I was really suspended in space," he said in an interview. Eventually, Kittinger began to hear the roar of the thickening atmosphere whipping past him. After deploying his primary parachute, Kittinger fell for over 9 minutes before he reached the ground. During his fall he experienced a minimum temperature of -94 degrees Fahrenheit and a maximum speed of 614 miles per hour, according to the National Museum of the Air Force.
  • Kittinger's jump set records for the highest balloon ascent, the longest parachute free fall and the fastest free fall speed. According to CBS News, two other men have died trying to recreate Kittinger's jump.
  • Since then, Felix Baumgartner has broken the speed and altitude record, but Kittinger STILL holds the record for longest free fall!
("Captain Joe Kittinger vs. the Stratosphere". This goes into some detail about the jump, but also about our atmosphere)
("Officials say sky diver broke the speed of sound" This is a video about Red-Bull-Sponsored Felix Baumgartner's record breaking jump from 128,000 ft, over 24 miles up.)

  • Brian Utley, a jump observer from the International Federation of Sports Aviation, said preliminary figures show Baumgartner reached a maximum speed of 833.9 mph. That amounts to Mach 1.24, which is faster than the speed of sound. No one has ever reached that speed wearing only a high-tech suit.
  • Baumgartner set the record on the 65th anniversary of the day man first traveled at supersonic speed in an aircraft (which was 1947)!
  • Baumgartner says that traveling faster than sound is "hard to describe because you don't feel it." With no reference points, "you don't know how fast you travel," he told reporters.
("Felix Baumgartner's Skydive spin as seen from camera on spacesuit")
("Felix Baumgartner makes record-breaking skydive from space"). Relive the moment.
("video of actual fall of Felix Bamgartner - multi angle with data")
baumgartner jump.jpg
("INSPIRATIONAL - Felix Baumgartner - Headcam footage space Jump!! FULL) (1:00)
("Mythbusters: Soccer ball shot from truck" - RElative velocity)

(A bunch of images and some videos of Baumgartner's historic jump).
(Graph of the terminal velocity of a sky diver)
(Chart of free fall motion)
(Link to physics classroom)
(picture of free-fall motion of an elephant and a mouse)
(article and graph discussing survival rate of cats falling from various heights - terminal velocity)

Department of Surgery, Animal Medical Center, New York, NY 10021
(High-rise syndrome in cats)
(Video of cat flipping over when falling. The writers of this page do not endorse the dropping of cats...just physics)
(image of wing suits)
wing suits.jpg
(GIF of backflip on skateboard)
(projectile motion demonstration from MIT)
(Projectile motion PHET. Simulates projectile motion with a computer program, including values, and can include air resistance)
(Where the images for how the velocity changes during a projectile's path came from) (0:19)
"Real or Fake? The World's Longest Basketball Shot")