Projectile Motion Exploration
1 Guided Practice
Teacher will break students up into groups of 3. Within each group, students will visit the PHET Projectile Motion Simulator. Students will also create a Google Doc to record their data and observations.
Part A: Predicting Range
- Students will make a table to record the initial velocity, height, and launch angle for 3 trials:
- Trial 1: 20 m/s, 0m, 25 degrees
- Trial 2: 10 m/s, 10m, 45 degrees
- Trial 3: 15 m/s, 4m, 60 degrees
- Students will add to their table calculated values for the range and time of the projectile. They will then use the simulator to get the actual values.
Part B: Predicting Initial Height
- Students will make a table to record the initial velocity, range, and launch angle for 3 trials:
- Trial 1: 13 m/s, 15m, 30 degrees
- Trial 2: 8 m/s, 9.3m, 55 degrees
- Trial 3: 19 m/s, 21.2m, 75 degrees
- Students will add to their table calculated values for the initial height and time of the projectile. They will then use the simulator to get the actual values.
Part C: Predicting Initial Velocity
- Students will make a table to record the initial height, range, and launch angle for 3 trials:
- Trial 1: 10 m, 20 m, 0 degrees
- Trial 2: 6 m, 15.5 m, 0 degrees
- Trial 3: 13 m, 6.5 m, 0 degrees
- Students will add to their table calculated values for the initial velocity and time of the projectile. They will then use the simulator to get the actual values.
Part D: Multiple Paths
- Students will make a table to record the initial height and range for 3 trials:
- Trial 1: 5 m and 18 m
- Trial 2: 12 m and 22 m
- Students will add to their table 3 different values for the launch angle, initial velocity, and time of the projectile that produce the given range with the given initial height. They will use the simulator to get their data.
- Students will include at least one screenshot of the simulator for their proposed combinations.
Conclusion: Students will answer the following questions:
1. What did you notice about the relationship between the launch angle and the initial velocity needed to hit the target with the same starting height?
2. What did you notice about the relationship between the time it takes to hit the target and the initial velocity and launch angle?
Key Standards Supported
Linear, Quadratic, And Exponential Models
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
For exponential models, express as a logarithm the solution to abct =dwherea,c,anddarenumbersandthebasebis2,10,ore; evaluate the logarithm using technology.
Interpret the parameters in a linear or exponential function in terms of a context.
Making Inferences And Justifying Conclusions
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Evaluate reports based on data.
Similarity, Right Triangles, And Trigonometry
Verify experimentally the properties of dilations given by a center and a scale factor:
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Key Standards Supported
Motion and Stability: Forces and Interactions
Plan and conduct an investigation to compare the effects of different strengths or different directions of pushes and pulls on the motion of an object.
Analyze data to determine if a design solution works as intended to change the speed or direction of an object with a push or a pull.
Plan and conduct an investigation to provide evidence of the effects of balanced and unbalanced forces on the motion of an object.
Make observations and/or measurements of an object’s motion to provide evidence that a pattern can be used to predict future motion.
Ask questions to determine cause and effect relationships of electric or magnetic interactions between two objects not in contact with each other.
Define a simple design problem that can be solved by applying scientific ideas about magnets.
Support an argument that the gravitational force exerted by Earth on objects is directed down.
Apply Newton’s Third Law to design a solution to a problem involving the motion of two colliding objects.
Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.
Ask questions about data to determine the factors that affect the strength of electric and magnetic forces.
Construct and present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects.
Conduct an investigation and evaluate the experimental design to provide evidence that fields exist between objects exerting forces on each other even though the objects are not in contact.
Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.
Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.
Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision.
Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.
Plan and conduct an investigation to provide evidence that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current.
Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials.