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5-34.

DeShawna and her team gathered data for their ball and recorded it in the table shown below.

Drop Height

Rebound
Height

$150$ cm

$124$ cm

$70$ cm

$59$ cm

$120$ cm

$100$ cm

$100$ cm

$83$ cm

$110$ cm

$92$ cm

$40$ cm

$33$ cm

1. What is the rebound ratio for their ball?

• Divide a rebound height by a drop height.

The ratio is about $0.83$.

1. Predict how high DeShawna’s ball will rebound if it is dropped from $275$ cm. Look at the precision of DeShawna’s measurements in the table. Round your calculation to a reasonable number of decimal places.

Multiply the drop height by the ratio.

2. Suppose the ball is dropped and you notice that its rebound height is $60$ cm. From what height was the ball dropped? Use an appropriate precision for your answer.

Divide the rebound height by the ratio.

1. Suppose the ball is dropped from a window $200$ meters up the Empire State Building. What would you predict the rebound height to be after the first bounce?

See part (b).

The rebound height is about $166$ m.

2. How high would the ball in part (d) rebound after the second bounce? After the third bounce?

• Continue multiplying the drop height by the ratio to find the next rebound heights.