Tip (all users): At the beginning, you may want to increase the y max value of the window settings in order to see the function being drawn and keep the collected data on the same graph.
TI-89,TI-89 Titanium, TI-92 Plus and Voyageé 200 users enter yn(x) = a* (x+h)^2 + k.
Note: If you have the Transformation Graphing application installed on your calculator, this is accomplished much easier by changing coefficient values directly on the graph screen. (There is no Transformation Graphing application for the TI-89,TI-89 Titanium, TI-92 Plus, or Voyageé 200.)
TI89/Titanium/92+/V200
TI83/84 Family

Activity 4—Bouncing Ball (cont.)

Parabolic

 

 

Explorations

The Distance-Time plot of the bounce forms a parabola.

ÊThe plot is in Trace mode. Press ~to determine the vertex of the first good bounce—a nice shape without lots of extra noise. Answer question 5 on the activity sheet.

ËSelect Main to return to the main screen. Choose Quit, and then select OK to quit EasyData.

ÌThe vertex form of the quadratic equation, Y = A(X – H)2 + K, is appropriate for this analysis. Press œ. In the Y= editor, turn off any functions that are selected. Enter the vertex form of the quadratic equation: Yn=A(XH)^2+K.

ÍOn the Home screen, store the value you recorded in question 5 for the height in variable K; store the corresponding time in variable H; store 1 in variable A.

For example (TI-83 & TI-84 Family users): Press 4 vtK Í, 2.5 vt H Í, 1 vtA Íto set K=4, H=2.5, and A=1.

ÎPress to display the graph. Answer questions 6 and 7.

ÏTry A = 2, 0, –1.Complete the first part of the chart in question 8 and answer question 9.

ÐChoose values of your own for A until you have a good match for the plot. Record your choices for A in the chart in question 8.

ÑRepeat the activity, but this time choose the last (right-most) full bounce. Answer questions 10, 11, and 12.

Advanced explorations

ÊRepeat the data collection, but do not choose a single parabola.

ËRecord the time and height for each successive bounce.

ÌDetermine the ratio between the heights for each successive bounce.

ÍExplain the significance, if any, of this ratio.

26 GETTING STARTED WITH THE CBR 2™ SONIC MOTION DETECTOR

© 1997, 2004, 2006 TEXAS INSTRUMENTS INCORPORATED

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Texas Instruments CBR 2 manual Advanced explorations, Distance-Time plot of the bounce forms a parabola

CBR 2 specifications

Texas Instruments has long been a prominent player in the field of educational technology, and the CBR 2 (Calculator-Based Ranger 2) is a testament to their commitment to enhancing the learning experience, particularly in the realms of mathematics and science. Designed to complement graphing calculators, the CBR 2 is a versatile data-collection device that empowers students and educators to explore real-world phenomena through hands-on experimentation.

One of the main features of the CBR 2 is its ability to capture a wide array of data through various sensors. The device is equipped with an array of built-in sensors that can measure motion, including speed and distance. This makes it an invaluable tool for physics experiments, allowing students to visualize concepts such as speed, acceleration, and trajectory.

The CBR 2 utilizes ultrasonic technology to detect distance through sound waves. This feature enables students to conduct experiments that demonstrate principles of sound and motion in a tangible way. With a range of up to 6 meters, the CBR 2 provides accurate and reliable measurements that can be graphically represented using compatible Texas Instruments graphing calculators.

The device is highly user-friendly, with simple interfaces that allow users to easily collect and analyze data. The integration with graphing calculators simplifies the process of data visualization, enabling students to create graphs in real time as they conduct experiments. This capability is particularly beneficial in encouraging interactive learning and fostering a deeper understanding of scientific principles.

The CBR 2 is designed to be portable and durable, making it suitable for classroom settings as well as outdoor experiments. Its compact size and lightweight construction ensure that it can be easily transported, allowing educators to take learning beyond the confines of the classroom.

The CBR 2 also supports various modes of data collection, including Event Mode, which allows users to trigger data collection based on specific events. This feature is useful in demonstrating concepts such as projectile motion and collisions, providing students with hands-on experience that enhances their learning.

In summary, Texas Instruments' CBR 2 is a powerful educational tool that enables students to collect, analyze, and visualize data in an engaging manner. With its built-in sensors, ultrasonic technology, and seamless integration with graphing calculators, the CBR 2 stands out as a versatile device that enriches the educational experience. It not only provides a platform for conducting experiments but also cultivates critical thinking skills and a deeper understanding of scientific concepts, preparing students for a future in STEM fields.