c How does gravity work on a body of mass in the air?
A
a 20 feet per second
B
b 8 feet per second
C
c It decreases, which makes sense. See solution.
Practice makes perfect
a The height the acrobat reaches depends on the time in the air. Therefore, time goes on the horizontal axis and height goes on the vertical axis. Let's plot the nine data points and connect them with line segments.
The acrobat's average velocity between 0.25 and 0.5 seconds is the slope of that segment. To determine the slope we want to divide the vertical distance by the horizontal distance between the segment's endpoints.
The slope between 0.25 seconds and 0.5 seconds is 20. Since the horizontal axis shows seconds and the vertical axis shows feet, we get a unit of feet per second. Therefore, her average velocity is 20 feet per second.
b To determine the average velocity between 0.5 and 1 second, we will draw a segment between these data points and calculate its slope.
The acrobat's velocity is 8 feet per second between 0.5 seconds and 1 second.
c As previously explained, the velocity of the acrobat is the same thing as the slope between two data points. As we saw from previous parts, the curve's slope is steep in the beginning of the jump and then gets less steep as the acrobat approaches maximum height.
Therefore, it must be that her average velocity decreases as the acrobat approaches the top of the jump. This makes sense, because if it did not then gravity would not work the way it is supposed to.
