Ashley, Stephanie, and Gena trop tennis balls from different heights, in feet. Then, they measure how high, in feet, each tennis ball bounces after it hits the ground. The table shows the measurements.

Question

Ashley’s Ball
Stephanie’s Ball
Gena’s Ball
Drop Height (in feet)
14
5
9
Bounce Height (in feet)
11
3
?


How high is Gena’s tennis ball likely to bounce after being dropped?
a.) 7ft
b.) 10ft
c.) 3ft
d.) 2ft

Answer 1

To determine how high Gena's tennis ball is likely to bounce, we can analyze the bounce heights relative to the drop heights of Ashley's and Stephanie's balls.

1. Ashley’s Ball:

   • Drop Height: 14 feet
   • Bounce Height: 11 feet
   • Bounce Ratio: \( \frac{11}{14} \approx 0.7857 \)

2. Stephanie’s Ball:

   • Drop Height: 5 feet
   • Bounce Height: 3 feet
   • Bounce Ratio: \( \frac{3}{5} = 0.6 \)

Now we can calculate a bounce ratio for Gena's Ball to understand what might be expected based on the bounce heights from Ashley's and Stephanie's:

Gena’s Drop Height: 9 feet

Now let's find a reasonable estimate based on the provided ratios. We'll assume Gena's bounce height will be somewhere between the ratios observed for Ashley and Stephanie:

1. Using Ashley's ratio (approx 0.7857), we calculate:

   • Estimated Bounce Height = \( 9 \times 0.7857 \approx 7.14 \) feet

2. Using Stephanie's ratio (0.6), we calculate:

   • Estimated Bounce Height = \( 9 \times 0.6 = 5.4 \) feet

Given that bounce heights will typically be lower than their drop heights, we can conclude that Gena’s bounce height will likely be between 5.4 feet and 7.14 feet, as per the other two examples.

The closest option to our estimated range is 7 feet.

Thus, the answer is: a.) 7ft