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Determine the launch velocity (v0) of a Projectile Launcher
Determine the launch velocity (v0) of a Projectile Launcher
Experimentation:
From the height of launch, calculate the time the marble will be in the air.
Align the launcher to 0˚(horizontal). Determine the velocity of your marble at 3 different settings.
Align the launcher to 90˚ (vertical). From a known (measurable height), determine the velocity of your marble at the 3 different settings.
Analysis:
Outline why the different marbles have different initial velocities?
Based upon your observations, measurements, and calculations, which of the two methods of determining the velocity of the marble is more reliable?
Before you begin experimentation, sketch the experimental setup and include where you will take measurements to collect data.
Pivot Interactive: Air Table Projectile Motion
Pivot Interactive: Air Table Projectile Motion
From the PIVOT Interactives activity, (link in GC). Collect data on the vertical and horizontal position of the puck. You will be making at least 3 graphs with the data, be sure to collect sufficient data to describe the relationships present.
Graph #1: y-position v. x-position
Graph #1: y-position v. x-position
On the SCATTER PLOT graph of the data:
Briefly describe the trends and shape of the graph.
Add an appropriate trendline:
the equation that describes the line.
the units of the trendline.
JAMBOARD Presentation:
Summarize your findings from your three graphs.
Answer the question (1, 2 or 3) that you were assigned.
Graph #2: x-position v. time
Graph #2: x-position v. time
On the SCATTER PLOT graph of the data:
Briefly describe the trends in the graph.
Add an appropriate trendline:
describe importance of the equation of that describes the line.
the unit of the trendline.
What evidence from your graph supports the following statement:
1. The sum forces in x-direction (horizontal) direction are zero.
Graph #3: y-position v. time
Graph #3: y-position v. time
On the SCATTER PLOT graph of the data:
Briefly describe the trends in the graph.
Add an appropriate trendline:
describe importance of the equation of that describes the line.
the unit of the trendline.
What evidence from your graph supports the following statement:
2. The puck is accelerating in a negative y-direction (vertical).
3. Based on the values derived from your graph, determine the angle at which the table is slanted.
Application of Concepts
Application of Concepts
Bullet fired horizontally:
Bullet fired horizontally:
Based on the data from the experiment and your data, suppose a gun fires a bullet from a height of h of mass m at a horizontal velocity of v. Air resistance on the bullet is negligible.
Sarah experimented with the original setup. She increased each variable independently, complete the table below to show how each would affect the range R of the bullet?
While measuring the range (R), she also measure the time for each trial. In the table below, show what relationship she would expect as she increased each of the variables.
Parabolic Motion Theory
Parabolic Motion Theory
2D Motion Data Collection and Analysis
2D Motion Data Collection and Analysis
Please consider the following scenarios and the implication of changing individual variables.
For each of the scenarios (6) below you will:
collect the data from the simulation above. Record your data in an appropriately constructed data table.
Create graph(s) of your data that illustrate the relationship between the variables explored. A minimum of the raw data graphed, plus any linearized graph that is appropriate.
Determine the appropriate mathematical equation to describe the relationships from your graphs. Be sure to include the meaning of the linearized slope.
∆height of launch
A massive, dense marble is shot horizontally (Θ = 0˚) from a launcher at height h with a velocity v. The marble is then launched at the same velocity v and angle Θ from various heights 2h, 3h and 4h.
The marble landed in a time of t when launched at velocity v from height h, determine the time to land from successive heights.
The marble had a range of R when launched at velocity v from height h, determine the range R for successive heights.
∆velocity of launch
A massive, dense marble is shot horizontally (Θ = 0˚) from a launcher at height h with a velocity v. The marble is then launched from the same height at various velocities (2v, 3v and 4v).
The marble landed in time t when launched at velocity v from a height h, determine the time to land in terms of v from successive velocities (2v, 3v and 4v)
The marble landed at range R when launched at velocity v from a height h, determine the range of the marble in terms of v from successive velocities (2v, 3v and 4v).
∆angle of launch
A massive, dense marble is shot from a height h of 0.0 meters at an angle Θ of 25˚ and velocity of v. The marble is then launched from various angles of Θ = 35˚, 45˚, 55˚, 65˚, 75˚, and 85˚ from a height of h and velocity of v.
The marble landed at range R when launched at a height h of 0.0 meters at an angle Θ of 25˚ and velocity of v, determine the ranges R for the subsequent launch angles.
The marble landed in time t when launched at a height h of 0.0 meters at an angle Θ of 25˚ and velocity of v, determine the time t for the subsequent launch angles.
Projectile Group Problem
Projectile Group Problem
Determine the range and maximum height of the golf ball when it is hit with the values determined by your group's birthdays.
Using sum of the days you were born (i.e. 10 March, 11 May, and 04 August you would choose a 25 meter cliff (10+11+04) and an initial velocity of 16 m/s ((03+05+08)+(10+11+04)) and an angle the sum of your birth months x 2 ((03+05+08)*2)=32˚ .
From a (sum of days)-meter cliff, Jasmine throws three aerodynamically perfect balls (no air resistance). Ball A is thrown upwards at (sum of months) m/s, Ball B is thrown downwards at (sum of months) m/s and Ball C is simply dropped from the height of (sum of days)-m.
Sketch the velocity time graph for each of the three balls. Indicate important aspects of each line (points, slope/gradient, and area under the curve)
Determine and rank the final velocity of the three balls upon impact with the ground.
Determine and rank the time of the three balls from release to impact with the ground.
Jasmine's sister has argued that the IB curriculum should be more realistic and include air resistance into their problems. For one of the three balls that was thrown, sketch a graph of the velocity v. time for a ball that experiences air resistance.
Projectile Practice Problems
Projectile Practice Problems
2016 Topic 2 Problems 2.1.pdf#25-36 of this problem set are projectile problems, please complete as many as necessary until you feel comfortable solving them. Solutions can be found HERE.
Bond Dropping onto a Train
Bond Dropping onto a Train
In the latest Bond movie, a cargo plane and a high-speed train are both approaching each other. Bond needs to jump from the plane onto the train. Due to his outfit, he is aerodynamically perfect (no air resistance).
Using realistic values (aside from the fact that he isn't wearing a parachute), determine when and where Bond should jump from the plane.
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