Lesson Plan 1
Title: Projectile Motion Lab: Range vs Launch Angle and Maximum Range
Prediction
i.
 Subject: Physics
 Estimated Time: 45minutes
 Grade Level: 9,10,11,12
Overview
 Summary of Events:
Students will perform a lab activity which investigates the fundamental physics behind
two dimensional projectile motion. A steel ball is launched from a high elevation to a
low elevation to see how launching angle affects range. The lab activity involves taking
measurements of a steel ball’s initial and final horizontal positions in order to illustrate
how the range changes as a function of launching angle. The launching angle is varied
from 30 to 50 degrees over five different angles. This lab allows the students to
investigate how the range changes as a function of launching angle. Furthermore, this
lab activity allows the students to predict and verify the range for an angle outside of
the 30-50degree interval using kinematic equations and position measurements. During
the range prediction portion of the lab the students will be given a toy figurine. They will
use the kinematic equations and vertical position measurements to predict where the
ball will land. They will then place the toy at the predicted landing spot and if they hit
the toy they get a treat.
 Materials List: (for each group)
o Projectile Launcher and Steel Ball
o Projectile Launcher Plunger Loading Rod
o Projectile Launcher Plumb Bob
o Independent Plumb Bob
o Meter Stick
o Measuring Tape
o Level Surface Bench
o Carbon Paper
o White Paper
o Safety Goggles
o Blue Masking Tape
o Steel Ball Catch Box(landing box)
o “C” Clamp
o Toy Figurine
o Treat(candy or some type of snack)
 Incorporated Standards:
 Safety Issues:
o
ii.
The projectile launcher is a spring loaded gun. It fires a 25mm steel ball, which is
around 55 grams, at high velocity. SAFETY GOGGLES MUST BE WORN AT ALL
TIMES.
o A plunger loading rod is to be used to engage the loaded spring in order to fire
the steel ball. NEVER allow anyone to stick their finger down the barrel of the
launcher to engage the spring. This can and will result in a finger being trapped
in the barrel. The only way to get the finger out is through further injury.
o NEVER allow any students to look down the barrel at anytime. This launcher is
to be treated as if it were a loaded gun. The launcher spring has enough force to
cause serious and permanent injury, especially to the eyes. SAFETY GOGGLES
MUST BE WORN AT ALL TIMES.
o NEVER allow students to walk in front of the launcher when it is loaded. This
includes putting hands, arms, legs, and faces in front of a loaded launcher.
o DO NOT fire the launcher without a ball this will break the spring.
Useful Information
 Background
o Galileo was the first known person to describe projectile motion correctly. He
noticed, unlike others before and during his time, that the motion of a projectile
was not a single motion, but two independent motions. He realized that the
motion could be broken into two components. From this analysis it could be
shown that gravity affected the vertical motion leaving the horizontal motion
unaffected. Furthermore, he drew his conclusions from the shape of the
projectile trajectory, which has an exact mathematical representation, namely a
parabola. From these observations and through a few corrections over time
scientists have developed what are known as the kinematic equations of
motion. Kinematics refers to the study of the motion of objects. The equations
which describe the parabolic motion incorporate several variables including
time, velocity, acceleration, and displacement. The parabolic motion is easily
seen from the second order term or the t2 term in the equations below. In real
life calculations of projectile motion one must consider air resistance, crosswinds, humidity, air pressure, elevation, and the motion of the earth known as
the coriolis effect in order to get accurate results over large distances. In this lab
we will assume an ideal projectile motion where the only factor we consider is
gravity. As you can see the physics behind projectile motion is very important in
many areas specifically aeronautics, astronauts and their shuttle reentry path,
pilots and flight plans, military and missile defense, mars landings, and even sky
diving!
o Some useful equations:
1. xf = xi + vixt + (½)axt2
2. yf = yi + viyt + (½)ayt2
3. vix=vcosθ
4. viy=vsinθ

5. R=(xf – xi)=vcosθ(vsinθ+(v2sin2θ – 2g(yf – yi))1/2)/g
6. Rmax=V2/g
7. Hmax=(V2sin(θ))/(2g)
Equations 1. and 2. are the kinematic equations for the x and y direction
respectively, these equations may be used to find the total time the ball spends
in the air. Notice ax should be zero and ay should be –g.
Equations 3. and 4. may be used to find the x and y components of initial
velocity based on the launch angle which is measured above horizontal.
Equation 5. is the equation for the range value regardless of launching and
landing elevation.
Equation 6. is the equation for max range when launching and landing elevation
are equal. This means a 450 angle gives the max range.
Equation 7. is the equation for max height of the projectile. This is for when
launching and landing elevations are the same, the students will have to add the
remaining height travelled based on their height measurements, when
launching from the table to the floor.(See picture in lab worksheet)
Vocabulary
1. Acceleration (a): this is the change in velocity per unit time, or how fast the
velocity is changing. This is a vector quantity and usually represented in meters
per second per second, m/s/s.
2. Acceleration due to gravity (g): this is a constant g. On Earth g=9.81m/s/s.
3. Axis: this refers to the horizontal(x-axis) or the vertical(y-axis) in a two
dimensional Cartesian coordinate system
4. Component: this refers to the projection of a vector along either the x-axis or yaxis. Usually this corresponds to x-component of a vector F being labeled as Fx.
Fx in most cases is defined as Fx=F*cos(angle), where cos is just cosine. Similarly
with the y component, Fy=F*sin(angle). See pictures on worksheet.
5. Displacement: This is the magnitude of the difference between initial and final
positions, the shortest distance between the two positions. This is a scalar
quantity.
6. Distance: this is the overall length of the path travelled. This is a scalar quantity.
7. Force (F): this is the outside influence which causes a mass to change its
direction, acceleration, or shape. In this case, direction and acceleration. This is
a vector quantity and usually represented in Newtons, which is a kilogrammeter per second per second, N=kg*m/s/s.
8. Gravitational Force (Fg): This is the force exerted by the mass of one object on
the mass of another object where both objects are separated by a certain
distance, in this case the Earth on the steel ball. This is a vector quantity.
9. Gravity: the phenomenon by which all objects with mass are attracted to one
another, this is what gives objects with mass weight.

10. Horizontal: this is the direction at which the gradient of the gravity at a point is
perpendicular, in other words the direction parallel to the ground and
perpendicular to the direction of gravity.
11. Kinematics: the study of objects in motion.
12. Landing Elevation: this is the height above the lowest point (usually the ground)
at which the steel ball lands.
13. Launch Angle: this is the angle above horizontal from which the steel ball is
launched out of the launcher.
14. Launch Elevation: this is the height above the lowest point (usually the ground)
from which the steel ball is launched.
15. Mass: a quantity which represents the amount of matter in a body, also you
could say the property of a body which represents the amount of resistance to
being accelerated by an external force. This is a scalar quantity and usually
represented in kilograms, Kg.
16. Origin: the crossing/intersection of the x-axis with the y-axis.
17. Range: This is the magnitude of the x-displacement of the projectile trajectory.
18. Scalar: a quantity which is described by a number.
19. Speed(S): this is the change in position per unit time. This is a scalar quantity
and is usually represented in m/s.
20. Two- Dimensional: This means two independent directions of motion. For
example horizontal and vertical motion or x and y motion.
21. Vector: a quantity which is described by a number and a direction.
22. Velocity (v): this is the speed and direction of an object. This is a vector quantity
and is usually represented in m/s with some directional coordinate or by a bold
letter.
23. Vertical: the direction which is aligned with the gradient of the gravity field,
rather the direction which is aligned with the direction of gravity.
24. X-direction: the direction parallel to the horizontal direction and perpendicular
to the y-direction.
25. Y-direction: in this case the direction parallel to the vertical direction and
perpendicular to the x-direction.
26. Weight: this is the force on an object due to gravity. One way to define this is
W=mg.
References/Resources
o Wikipedia, this is a great resource if you want a fast and general understanding
of most physical topics.
o Hyperphysics, this is a website about physics created by Georgia State
University, also a great website for fast and a bit more detailed physics topics.
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
o A great book which many undergraduate science majors use and my
undergraduate professor helped write is, Physics for Scientist and Engineers, 4th
edition, Douglas C. Giancoli, 2008. This will be a higher level of math, but has a
lot of good examples and homework problems.
iii.
Lesson Outline
 General Introduction(5-10min depending on if you use the video)
o Whiz Bang
 Video on youtube “Mr. Physics: Projectile Motion (Episode 2)” up to
4:57. Do this after gauging audience.
o Audience and Knowledge Review(5min)
 Who know’s or can give me an example of projectile motion?(a ball
being thrown, or something like a sky diver, or a cannon, or a bullet
being fired, or someone hitting a golf ball etc.)
 If that fails try, how many of you have seen a baseball player hit a
baseball, or have seen someone throw a ball? What kind of shape did
the ball make with its flight path?(looking for curved, parabolic, etc.)
 Who knows what a force is or can give me an example of a force?(
looking for a push or pull, or gravity, etc.)
 Does anyone know a formula for force?( F=ma)
 What force made that ball make that shape?(gravitational force)
 Ok, what is gravity? What is the gravitational force? What is the
acceleration due to gravity?(see vocabulary above)
 What if we wanted to know the height the ball reaches in its trajectory?
What formula could we use for that situation?(y kinematic equation)
 Okay so we have a formula for the height of the ball, what if we wanted
to know the range, or how far the ball traveled from the person
throwing or hitting it?
 We need to find the range or the displacement, does anybody know a
formula for that?( Start with the x kinematic equation and derive the
range equation)
o Transition Sentence
 Do you think the angle the ball is hit or thrown from will affect how far
it will fly, HOW? What angle do you think will give you the maximum
range value? PLAY THE VIDEO THEN SAY, Ok well in front of everyone
there is a lab worksheet and at the back of the room are the lab
supplies. Today we are going to see what angle really gives the
maximum range and see if your predictions are correct. (Remember to
not answer these questions for them, the lab will do this. now walk
them through the step by step procedure.)
 Instructional Transition
o Inquiry Activity(35-40min)
a) Transition Sentence: The sentence above starting with Today…
b) Worksheet( have the group worksheets already out and then hand them
the homework worksheet as they go out the door or sometime towards
the end, don’t want to overwhelm them with work before they finish)
iv.
v.
vi.
vii.
viii.
Assessment
 The assessment questions are included in the introduction and throughout the lab
activity and at the end of the lab activity, see the Audience section and the lab
worksheet and the homework worksheet.
 Some additional questions to pose to groups along the way are the following:
o What is the horizontal acceleration( zero)? What is the vertical acceleration(-g)?
o Why is the horizontal acceleration zero?(because the force of gravity acts
downward and thus the acceleration of gravity acts downward so no horizontal
acceleration)
o Should we be considering the friction of the launcher tube in our calculations?
(yes, because there is some friction but it is very small)
o Is the time the ball travels in the x-direction the same as the time the ball travels
in the y-direction?(yes, show this with a picture, or ask someone to show why
this is true with a picture)
o There are more, just have to be creative and pick apart the math and relate it to
the physics.
Closure(5min)
 The wrap up should address the fact that gravity affects the y component of velocity and
not the x-component of velocity because of the direction of the force of
gravity/acceleration due to gravity. It should also include a statement about how the
angle affects the range when the launching elevation is different from the landing
elevation, i.e. the 450 is not the angle that produce max range unless the launching
angle is the same as the landing angle. Then the last sentence could be something like,
“I passed out a homework sheet to everyone and I want you to finish this by such and
such date, we will go over the answers in class next time.” Or maybe introduce the idea
of a third dimension, “So today we worked with x and y dimensions, what would happen
if we had a fan blowing across the balls flight path? (We would need to consider the
third direction, the z-direction. This is what airline pilots have to incorporate into their
calculations when making a flight plan. They may encounter strong cross-winds that
force them to head in a different direction so they don’t waste too much fuel. We talk
about this in the next lesson.)”
Modifications
 See Extended Time
Contingencies
 Drawing on the board is always a good tool for this type of lab
Extended Time(5-20min depending on how much time you have left)
 This lab is already long, but you could incorporate the following:
o
o
o
Have them predict the range and verify for a larger or smaller angle outside of
the 30-50 degree range( part B)
Change the elevation of the landing box ( part C)
Start the homework sheet early