Donald is flying a kite at the beach on a windy day. He begins to pull the kite back in and, as he does, the kite descends.

Question

There is a linear relationship between the time, in seconds, since Donald began pulling the kite in and its height, in feet.
Time (seconds) Height of kite (feet)
0 120
12 111
24 102
36 103
Describe the rate of change for this relationship.
The height of the kite
by
per second.

Answer 1

To describe the rate of change for the relationship between time and the height of the kite, we need to examine the changes in height over the changes in time.

Let's calculate the average rate of change based on the provided data points.

From the data:

1. From 0 seconds to 12 seconds:

   • Change in height = 111 - 120 = -9 feet
   • Change in time = 12 - 0 = 12 seconds
   • Rate of change = \(\frac{-9 \text{ feet}}{12 \text{ seconds}} = -0.75 \text{ feet per second}\)

2. From 12 seconds to 24 seconds:

   • Change in height = 102 - 111 = -9 feet
   • Change in time = 24 - 12 = 12 seconds
   • Rate of change = \(\frac{-9 \text{ feet}}{12 \text{ seconds}} = -0.75 \text{ feet per second}\)

3. From 24 seconds to 36 seconds:

   • Change in height = 103 - 102 = 1 foot
   • Change in time = 36 - 24 = 12 seconds
   • Rate of change = \(\frac{1 \text{ foot}}{12 \text{ seconds}} = \frac{1}{12} \text{ feet per second} \approx 0.0833 \text{ feet per second}\)

Overall, for most intervals, the kite is descending at a rate of \(0.75\) feet per second, except in the last interval where it briefly ascends at a rate of about \(0.0833\) feet per second.

In summary, the height of the kite decreases by approximately 0.75 feet per second for the first two intervals and then increases slightly by about 0.0833 feet per second in the last interval.