Arun launches a toy rocket from a platform. The graph below shows the height of the rocket hh in feet after tt seconds. Find the interval for which the rocket’s height is decreasing.

Question

0
Time (in seconds)
Height (in feet)
t
h
0
Time (in seconds)
Height (in feet)
(1.75, 169)

Answer 1

To determine the interval during which the rocket's height is decreasing, we would typically analyze the graph of height \( h \) with respect to time \( t \). Since the specific graph isn't provided here, I can guide you on how to interpret a height vs. time graph.

1. Identifying Decreasing Intervals: Look for sections of the graph where the height \( h \) is falling as time \( t \) progresses. These are intervals where the slope of the graph is negative.

2. Example Analysis:

   • If you observe the graph and see that the height is at its peak and then begins to decline, note the time intervals before and after this peak.
   • For instance, if the peak height occurs at \( t = 1.75 \) seconds and the height is decreasing after that, you might look at the interval starting from \( 1.75 \) seconds until the rocket reaches the ground (height \( h = 0 \)).

If the peak height occurs at \( (1.75, 169) \), then you can conclude that the height is decreasing for the time period after \( 1.75 \) seconds until it reaches the ground level.

For instance, if the rocket reaches the ground at some time \( t \), you would define the interval as \( (1.75, t) \) seconds, where \( t \) is the time when \( h = 0 \).

If you have further details from the graph you are analyzing, or if there are specific points of interest that you see on the graph, feel free to share, and I can give a more tailored response!