Physics Unit 2 – Two Dimensional Motion and Force – Projectile Motion
HSCE
P1.1C: Conduct scientific investigations using appropriate tools and techniques.
P2.2g: Apply the independence of the vertical and horizontal initial velocities to solve projectile motion problems.
P2.2g: Solve problems involving force, mass and acceleration in two-dimensional projectile motion restricted to an initial horizontal velocity with no initial vertical velocity (e.g., a ball rolling off a table).
Background
The motion of an object moving both horizontally and falling freely under the influence of gravity is referred to as projectile motion. Though the horizontal and vertical motions occur simultaneously, they are otherwise independent of each other. Since there is no horizontal component of acceleration, the velocity in the x-direction will be constant. Likewise, the vertical component of the motion should be that of free-fall.
Useful constants and equations:
g = 9.8 m/s2
ΔX = V0Xt
ΔY = V0yt - ½gt2
Common Student Misconceptions:
Students are frequently unable to grasp the independence of motion and force in the X and Y directions. Many will not realize that X motion is an example of constant speed, while Y motion is an example of constant acceleration.
Vocabulary
· Acceleration due to gravity
· Free-body diagrams
· Horizontal velocity
· Initial Velocity
· Mass
· Net Force
· Projectile
· Projectile motion
· Range
· Trajectory
· Velocity
· Vertical velocity
Suggested Materials (per group)
Tennis ball
Measuring Tape
Meter Stick
Stopwatch
Flag to mark point of impact - optional
Procedure – 50 minutes
1. In groups (ideal n = 3), students determine the best way to measure range, time and initial height.
2. Students launch projectiles (tennis balls) by throwing them. They should attempt to achieve maximum range.
3. Each student should launch and record data for one projectile. The groups are to help measure the results. Each student will make calculations based on his or her own data.
4. Each student should calculate launch angle and velocity (initial velocity, as well as the horizontal and vertical components of initial velocity) for his or her throw.
5. Each student should plot velocity vs. time graphs for the horizontal and vertical components of the trajectory.
How to Incorporate More Inquiry
· Do not prompt the students to measure range, time and initial height. These are all necessary for the calculations and are the only measurable values with the provided materials.
Conclusions
Additional questions:
· Based on your calculated initial velocity, determine your maximum possible range. Why didn’t your throw go this far?
· How are the shapes of your two graphs different from one another? What does this imply about the motion of your projectile?
Formative Assessment Ideas:
· What factors can affect the trajectory of a projectile?
· Which of these factors can you control as you throw?