Projectile Motion

Table of Contents

Motivation & Context: To understand nature

Introduction: Flash Animation and Flash 8 video with Audio Explanation

Java Interactive Activity: Learning by doing

Quiz: Java feedback to guide thinking process and promote making sense.

 

Motivation & Context:

 

The physics of sports is fun, and I encourage everyone to dabble in the scientific underpinnings of their favourite sport. It is also worth bearing in mind that sport is now big business, and it is possible to make a career in the physics of sport if you are keen enough. While in most instances scientists cannot improve the performance of elite athletes, they can make a significant contribution to sports engineering, such as designing better sports equipment and training devices. And who knows, maybe the top sportspeople might be curious to understand the science underlying their performances.

source: http://physicsweb.org/dl/PWJUNE06linthorne.pdf

Discus, javelin, shot, and hammer throwing are Olympic field events involving projectiles. Other Olympic events involve jumping. For example, while competitors in the long jump frequently hurl themselves over 7 m into a sandpit, ski jumpers can travel over 100 m between take-off and landing.

Discus, javelin, shot, and hammer throwing are Olympic field events involving projectiles. Other Olympic events involve jumping. For example, while competitors in the long jump frequently hurl themselves over 7 m into a sandpit, ski jumpers can travel over 100 m between take-off and landing.

source: Absorb Physics for A-Level by Adrian Watt

 

Introduction: Flash Animation video with Audio Explanation

 

 

source: http://www.archive.org/details/AP_Physics_B_Lesson_02

Quiz to recap the main points:

A B C

Purpose of this question: To be able to use a for the initial velocity and a for final velocity

a

 
A B C

Purpose of this question: Some students feedback, they never learn s = u t + 0.5 a t^2 and v = u + a t. link to explore Equations of motion under constant acceleration. Select 2.

For the time being, you should be able to use unit analysis, ( compare the units of the terms) to conclude the possible equation. :)

Recalling these are Equations of motion and later expand to x and y components separately. So from these 2 equations, we can get 4 equations which can be used to solve ALL projectile motion problems. COOL right? a and a

 

 

a

A B C

Purpose of this question: Some students feedback, they wonder why ay= - g link to explore Equations of motion under constant acceleration. Select 4.

writting in the form above or like in this form, allows you to recall by association a for both formula a and a

 

 

 

How is the a initial angle of u (initial velocity a.k.a. a here) here used?

A with the positive x-axis counterclockwise
 B with the positive y-axis anti-counterclockwise
 C doesn't really matter, any angle also can.

purpose of this question: To facilitate the understanding of the angle of launch is always a, positive x-axis counterclockwise. For clarity of solution, the angle a is the angle made by the final velocity to the positive x-axis counterclockwise. Thus, s and a
 
 

 

A B C
Purpose of this question: writting in the form above or like in this form, allows you to recall by association a for both formula a and a

 
Memorize only useful and meaningful formulae ONLY, the rest is thinking skills.
Memorize more formulae, it is what PHYSICS problem solving means.
Question 10: Assuming the angle a= 35 degree, given u = 100 m/s, find the a given the ground is perfectly horizontal.

 

hint: a and a
 step one: let the origin be the point of release of projectile

step two: fill in the end condition into the 2 equations (which is actually four equations if you think about x and y direction independently)

hint: in this particular case, a and a = 0 can be used.

step three: think and decide what you need and how to solve the problem

hint: need pen and paper to do this

aand a

A a = 958 m
B a = ?
purpose of this question: To facilitate the solution of projectile motion, in easy and simple steps, building the confidence to solve more complex problems later.

 

 

 

Java Interactive Activity: Learning by doing

This Java applet shows the motion of a projectile.

The "Reset" button brings the projectile to its initial position. You can start or stop and continue the simulation with the other button. If you choose the option "Slow motion", the movement will be ten times slower. You can vary (within certain limits) the values of initial height, initial speed, angle of inclination, mass and gravitational acceleration. The radio buttons give the possibility to select one of five physical sizes.

The effect of air resistance is neglected.

source: © Walter Fendt, September 13, 2000 http://www.walter-fendt.de/ph11e/projectile.htm

 

need help using the applet below ? click here to go to guide to applet
 

Guide to using applet :

Click on this link !

 

Quiz: Java feedback to guide thinking process and promote making sense:

Question 1: A projectile is an object upon which the only force acting is gravity. assuming that the influence of air resistance is negligible, what are the motion that are projectile below? a
  source: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/vectors/u3l2a.html
A an object which is thrown vertically upward
 B an object is which thrown upward at an angle
 C any object which once projected continues in motion by its own inertia and is influenced only by the downward force of gravity
 D an object is which has a constant horizontal force being constantly applied to the object like a rocket who is constantly experiencing exhaust gas being expelled.

purpose of this question: To set the assumptions of projectile in idealized context. We are not discussing more complex motion like arrows that have wings that produced a force called "LIFT" to prolong the time of flight.

  • Only the force of gravity acts on the vertical motion.

  • No frictional forces impede the horizontal motion

 

 
Question 2: The projected object (projectile) immediately after leaving the hand that throws it,  

source: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/vectors/u3l2a.html

A only experience the force of gravity vertically downwards
B experience the force of continuity in the x-direction as well because force causes motion
purpose of this question: To set the assumptions of projectile in idealized context.

 

 

Question 3: The apparatus shown can be used to drop the blue ball vertically while simultaneously projecting the orange ball horizontally The projected ball and the ball dropped vertically hit the floor at …

A exactly the same instant
 B different times.

purpose of this question:

The blue ball is dropped vertically. In equal time intervals the distance it travels increases, so the ball is accelerating as it falls. The blue ball is freely falling due to the force of gravity, so its acceleration vector a=a  ms−2

 

Question: An object of greater mass will fall at a greater rate than an object of lesser mass


True
 False
purpose of this question: acceleration vector a=a  ms^−2 . Notice ay = -g has no mass involved. You can verify this by doing your own experiement, take a book and a piece of paper drop them with the small piece of paper above the book, using the book to shield the effects of air resistance, and you will notice something interesting......... The book and the small piece of paper accelerates at the same acceleration.

 

Question 4: A cannonball shot horizontally from a very high cliff at a high speed. And suppose for a moment that the gravity switch could be "turned off" such that the cannonball would travel in the absence of gravity?

What would the motion of such a cannonball be like?

source: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/vectors/u3l2a.html

A According to Newton's first law of motion, such a cannonball would continue in motion in a straight line at constant speed. In the absence of all forces, "an object in motion will ...". This is Newton's law of inertia.
 B It cannot move because no force equals no motion, so it will stationary despite given a initial velocity by the cannon's gunpowder

purpose of this question: To demonstrate the misconception: " force produces motion" to understand it is possible to have motion without force in relation to Newton's Law of Inertia ( N1stL ). which states

"An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force."

 
Question 5: Consider a cannonball projected horizontally from a cannon from upon a very high cliff. In the absence of gravity, the cannonball would continue its horizontal motion at a constant velocity. This is consistent with the law of inertia. And furthermore, if merely dropped from rest in the presence of gravity, the cannonball would accelerate downward, gaining speed by a rate of 10 m/s every second. This is consistent with our conception of free-falling objects accelerating at a rate we call the "acceleration of gravity." a

source: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/vectors/u3l2a.html

A The vertical force acts perpendicular to the horizontal motion and will not effect it ("perpendicular components of motion are independent of each other").
 B the projectile travels with a constant horizontal velocity and a downward vertical acceleration.

purpose of this question: to justify why it is possible to analyze the motion independently in x and y directions, elegantly represented as a and a

 
Question 6: Now suppose that our cannon is aimed upward and shot at an angle to the horizontal from the same cliff. In the absence of gravity (i.e., supposing that the gravity switch could be "turned off") the projectile would again travel along a straight-line, inertial path. An object in motion would continue in motion at a constant speed in the same direction if there is no unbalanced force. This is the case for an object moving through space in the absence of gravity. However, if the gravity switch could be "turned on" such that the cannonball is truly a projectile, then the object would once more free-fall below this straight-line, inertial path. In fact, the projectile would travel with a parabolic trajectory. The downward force of gravity will act upon the cannonball to cause the same vertical motion as before - a downward acceleration. The cannonball falls the same amount of distance in every second as it did when it was merely dropped from rest (refer to diagram below). Once more, the presence of gravity does not effect the horizontal motion of the projectile. The projectile still moves the same horizontal distance in each second of travel as it did when the gravity switch was "turned off."

source: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/vectors/u3l2a.html

A The force of gravity is a vertical downward force and does not effect horizontal motion
 B perpendicular components of motion are dependent of each other
purpose of this question: to justify why it is possible to analyze the motion independently in x and y directions, elegantly represented as a and a
Question: Use the applet, for the same initial speed u, at initial height = 0, explore when the projectile is shot out at angle of 15 degree, what is the other angle that results in the same horizontal displacement?

75 degree
60 degree
45 degree
30 degree
purpose of this question: Experiment by doing, now try a different angle say, 35 degree, did you get the other angle to result in same horizontal displacement to be 55 degree ? What is the generalisation you can conclude ?? Conduct your own scientific inquiry and explore this !!!
   

 

http://www.mhhe.com/physsci/physical/giambattista/proj/projectile.html

Question: A hunter shoots a coconut held by a monkey that drops from rest vertically down from a tree. Given that at the moment the monkey drops the cococnout and at the same instant the hunter shoots, where should the hunter aim in order to hit the coconut released by the monkey?a

Above the coconut
At the coconut
 Below the coconut

purpose of this question:This kind of question used to be for high mathematical ability students because to prove this idea, YOU need mathematical vigor to show that.. Mr Wee thought it is a good idea to expose YOU to interesting facts about projectile motion. For more interested students, Google search it and share your findings with the class.
 

 

A small car will roll to the right at constant speed. It fires a ball straight up as it continues to move. After the ball is fired, will it come down

A Ahead of the car
B On top of the car
C Behind the car
purpose of this question: Using video and demonstration, we can verify physics, mathematics and real life observation to be consistent. Do you know why it is so? Discuss with your friends and see if you share the same viewpoints.
 

 

 

 

 
Question 7: assuming on a horizontal ground, the velocity of the projectile just before hitting the ground is
A a
 B a equal to zero because it hit the ground

purpose of this question: To demonstrate the misconception of the speed after hitting the ground roll and bound a few times is NOT part of a projectile motion, because the contact force from the ground acting on the ball change the motion to an accelerated motion upwards.

It is the "speed of JUST before hitting the ground" that is still projectile.

   
Question 8: Now in this unit we will apply both kinematics principles (Equation of motion under constant acceleration, a and a) and Newton's laws of motion to understand and explain the motion of objects moving in two dimensions. In short, we only need these 2 equations which can be expressed in 2 directions ( + x direction and + y direction ), tapping on our understanding of the cartesian coordinate system in mathematics.

a


 a

note: we using this equations, we need to assume the origin (0,0) is the start of the projectile motion, due the assumption of a = (0,0)

purpose of this question: To facilitate the progression of kinematics equations of motion under constant acceleration to be vectors into projectile equation of motion in 2- dimensional analysis, un accelerated motion in x -direction and uniform accelerated motion in negative y direction.
 
 

 

Question11: The motorcycle is traveling horizontally at take-off. In flight it follows a projectile path, so we can treat its vertical and horizontal motions separately. To reach the landing-zone the bike must travel 48 m horizontally in the same time as it travels 19.62 m vertically. Use the animation to determine the horizontal speed required to land in the center of the landing-zone.

The horizontal speed required to land in the center of the landing-zone is …

source: Absorb Physics for A-Level by Adrian Watt

hint: a and a
 step one: let the origin be the point of release of projectile

step two: fill in the end condition into the 2 equations (which is actually four equations if you think about x and y direction independently)

hint: in this particular case, a= 48 m and a = -19.6 m can be used.

step three: think and decide what you need and how to solve the problem

A 10 ms^−1
 B 24 ms^−1
 C 28 ms^−1
 hint: The angle a = 0 degree because the motorcycle is launch with the speed a which is a

purpose of this question: To facilitate the solution of projectile motion, in easy and simple steps, building the confidence to solve more complex problems later.

 
Question 12: What is the condition for the cannonball to always hit the target set 20 m away from the cannon? The flash allows you to verify your answer or the Java Interactive Activity: Learning by doing early also allows you to check.

source: Absorb Physics for A-Level by Adrian Watt

hint: a and a
 step one: let the origin be the point of release of projectile

step two: fill in the end condition into the 2 equations (which is actually four equations if you think about x and y direction independently)

hint: in this particular case, a= 20 m , a = 0 m a= - a can be used.

step three: think and decide what you need and how to solve the problem

mathematical identity needed: a

A a which helps us understand the minimum speed for the projectile is u = 14 m/s
B False

purpose of this question: To facilitate the solution of projectile motion, in more mathematical and systematical steps versus trial and error method. Note that the flash programing is not accurate, the java is accurate.

This tells me an important lesson about the internet, not everything is correct and accurate, we have to verify the accuracy of content.