A balloon is released from the top of a building. The graph shows the height of the balloon over time. What is the rate of change of the height with respect to the time for the balloon?
The rate of change of the height with respect to time for the balloon is -10 m/s.
Explanation:
Looking at the graph, we can see that the height of the balloon decreases as time increases. This means that the balloon is descending or falling down. The rate at which the balloon is falling down can be determined by finding the slope of the line tangent to the graph at any given point. The slope of this line represents the rate of change of the height with respect to time.
Using the slope formula, we can find the slope of the line tangent to the graph at two different points and then take their average to get an approximate value for the rate of change. For example, if we choose two points on the graph (t1, h1) and (t2, h2), then the slope of the line through these points is given by:
slope = (h2 - h1) / (t2 - t1)
Using this formula, we can calculate the slope for different pairs of points on the graph and then take their average to get an approximate value for the rate of change.
Solution:
From the given graph, we can see that at t=0 seconds, the height of the balloon is 50 meters. At t=5 seconds, the height of the balloon is 0 meters. Therefore, using these two points on the graph, we can calculate the slope as follows:
slope = (h2 - h1) / (t2 - t1)
= (0 - 50) / (5 - 0)
= -10
Therefore, the rate of change of the height with respect to time for the balloon is -10 m/s.
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castiedd001
I tried to answer that but it was incorrect, the answer was actually 1/10
Answers & Comments
Answer:
The rate of change of the height with respect to time for the balloon is -10 m/s.
Explanation:
Looking at the graph, we can see that the height of the balloon decreases as time increases. This means that the balloon is descending or falling down. The rate at which the balloon is falling down can be determined by finding the slope of the line tangent to the graph at any given point. The slope of this line represents the rate of change of the height with respect to time.
Using the slope formula, we can find the slope of the line tangent to the graph at two different points and then take their average to get an approximate value for the rate of change. For example, if we choose two points on the graph (t1, h1) and (t2, h2), then the slope of the line through these points is given by:
slope = (h2 - h1) / (t2 - t1)
Using this formula, we can calculate the slope for different pairs of points on the graph and then take their average to get an approximate value for the rate of change.
Solution:
From the given graph, we can see that at t=0 seconds, the height of the balloon is 50 meters. At t=5 seconds, the height of the balloon is 0 meters. Therefore, using these two points on the graph, we can calculate the slope as follows:
slope = (h2 - h1) / (t2 - t1)
= (0 - 50) / (5 - 0)
= -10
Therefore, the rate of change of the height with respect to time for the balloon is -10 m/s.