Applied Parabolas: Catapult (one test grade)
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1 Name: I. Overview: PreCalculus Applied Parabola Project Applied Parabolas: Catapult (one test grade) You will use catapults to launch candy into the air. Using a stopwatch, you will time how long the projectile is in the air That time will then be used to find an equation to model the flight of the candy. Then the catapult will be moved to the top of a desk, and you will use your equation to estimate how far the projectile will travel. Points will be scored based on how close your candy comes to landing on a target that you will place on the floor. You will only have four attempts once the catapult is placed on the desk. Note: You will lose significant points if you break the catapult. You will lose significant points if you eat the candy or throw it around the room. II. Getting the Data: For each trial launch, fill in the distance traveled and the time in the air. Trial Number Average: Total Time in the Air (seconds) Total Distance traveled from launch to landing (inches) - -
2 III. Calculating the Parabola: PreCalculus Applied Parabola Project. Convert the Average Distance found in Step II. from inches to feet: Average Distance (inches) = inches/feet = feet. Calculating the Vertex of the Parabola: Total Distance (vertical) Total Distance (horizontal) Average Time (seconds) Average Distance a. Time in the air is both rising and falling time. The peak of the parabola we are trying to calculate is the halfway point in time. Time To Parabola Peak (seconds) = TotalTime = (seconds) b. To get the Vertical Distance, we will use physics to calculate the height of the parabola (i.e., the vertical distance of the candy from the ground, at it s peak). height height (vertical distance in feet) = This is the y-value of your vertex. g t where g = gravity = feet/second t is the time to parabola peak you just calculated ( ) ( ) ( ) = - -
3 c. To get the x-value of your vertex: PreCalculus Applied Parabola Project (The Average Total Distance traveled from launch to landing) = (ft) = (ft) d. Vertex of your parabola = (, ) Vertex (x, y). Vertex Form y a( x h) k Review: When a >, the parabola opens When a <, the parabola opens Vertex variables in the Vertex Form: (, ) Vertex you calculated: (, ) a. Re-write the Vertex Form with your vertex in the equation: y = a (x - ) + b. If the launcher was at point (,), plug this point into the vertex form equation with our calculated vertex: c. Now solve for a: = a ( - ) + d. Now, write your vertex form equation, using the a-value you just calculated and the vertex point you calculated before: y a( x h) k y = ( x - ) + = e. Convert to Standard form: f. What is the y-intercept: - -
4 IV. Graphing the Parabola: Use your equation from the previous step, plug in the x-values from the table below and calculate the y-values. Show your work here: a. X Y Solve for the x-intercept: Set y = and solve for x Use the Average Total Distance (horizontal) you found earlier Don t forget the ± values for x b. Plot the points you just calculated Label the axes. c. What are the x-intercepts? d. What are the y-intercepts? e. Is this the same y-intercept you calculated before? - -
5 f. Why don t we need to show the other quadrants on the graph? g. What happens if we choose a negative x-value? h. What does it mean to get a negative y-value on our graph (in real-world terms)? i. What do to get when you choose a positive x-value that is much bigger than the distance your candy traveled? j. What does this mean with regards to our parabola (in real-world terms)? V. Translating the Parabola:. Measure the distance from the floor to the top of the table (inches) Distance (inches) Distance. Add the distance (in feet) to your k value in your vertex equation: y a x h k D feet ( ) ( ) y = ( x - ) + +. Re-write your vertex equation here:. Convert to Standard form: 5. What is the y-intercept: - 5 -
6 5. Re-plot the parabola using these x - y values. Label the axes. Show your work here: X Y Solve for the x-intercepts: Set y = and solve for x Don t forget the ± values for x VI. Making a Prediction:. Based on your calculations in Part V. where do you think the candy will land when it is launched from the top of the table? (hint: what are the x-intercepts?) (feet from the table) Once you have a valid prediction, get Ms. Wilson to place the target at your predicted spot
7 Shot Distance (inches) Distance. What is your average distance (in feet) =. How close is your average distance from the distance you predicted (the target)?. How close are your individual distances to your predicted distance? 5. What could you have done to improve your results? - 7 -
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