Concept Byte: Collecting Linear Data

Use With Lesson 5-7

ACTIVITY

In this activity, you will release a ball from different heights and record the maximum height after its first bounce. Complete this activity over a hard surface. Measure all heights from the bottom of the ball.

ACTIVITY

Place one end of a meter stick on the floor and tape it to the wall. Tape a second meter stick to the wall starting at the top of the first meter stick.

1. Data Collection Drop the ball from 50 cm. Carefully record its maximum height after the first bounce. Repeat.
2. Copy and complete the table below. You may make additional measurements using different starting heights.
3. Graph the data from both trials on the same coordinate plane.
4. Reasoning Why is it reasonable to use (0, 0) as a data point?

5. Draw a trend line that includes (0, 0).

   Bounce Height Data

   Initial Height (cm)	Maximum Height After First Bounce
   	Trial 1	Trial 2
   50	□ white square	□ white square
   100	□ white square	□ white square
   150	□ white square	□ white square
   200	□ white square	□ white square

6. 1. Predict Use your line to predict the maximum height of the first bounce after the ball is dropped from 175 cm.
   2. From what height would you have to drop the ball for it to reach 2 m after the first bounce?
7. 1. Use a graphing calculator to find the equation of the line of best fit for the data in the table.
   2. Predict Use your equation to predict the maximum height of the first bounce after the ball is dropped from 175 cm.
   3. How do your predictions from part (a) of Step 6 and part (b) of Step 7 compare?

Exercises

8. Multiple Choice The graph below shows the bounce data for a ball.

   Let x = the initial height in centimeters. Let y = the maximum height in centimeters. Which equation best models the data?

   
   Image Long Description

   1. y = 0.3 x y equals 0.3 x
   2. y = 0.4 x y equals 0.4 x
   3. y = 0.5 x y equals 0.5 x
   4. y = 0.6 x y equals 0.6 x
9. Suppose students used several different types of balls and found that the slopes of the trend lines were not the same. What is the significance of the slope?

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