Question

1. the height of a rocket, at selected times, is shown in the table below. based on these data, which statement is not a valid conclusion? 1) the rocket was launched from a height of 180 feet. 2) the maximum height of the rocket occurred 3 seconds after launch. 3) the rocket was in the air approximately 6 seconds before hitting the ground. 4) the rocket was above 300 feet for approximately 2 seconds.

Explanation:

• Option 1: At time \(t = 0\) (launch time), the height \(h=180\) feet. So, the rocket was launched from a height of 180 feet. This is a valid conclusion.
• Option 2: Looking at the height values \(180,260,308,324,308,260\), the maximum height is \(324\) feet which occurs at \(t = 3\) seconds. This is a valid conclusion.
• Option 3: There is no data point at \(t=6\) seconds. Also, the data pattern shows that the height is decreasing after \(t = 3\) seconds, but we cannot assume that it will hit the ground at \(t = 6\) seconds based on the given data. The data only goes up to \(t = 5\) seconds. This is not a valid conclusion.
• Option 4: The height is above \(300\) feet at \(t = 2\) (\(h = 308\)), \(t=3\) (\(h = 324\)) and \(t = 4\) (\(h = 308\)). The time interval from \(t=2\) to \(t = 4\) is \(4 - 2=2\) seconds. This is a valid conclusion.

Answer:

1. The rocket was in the air approximately 6 seconds before hitting the ground.