Question 6 • Advanced Algebra: Concepts and Connections
An acorn falls from the branch of a tree to the ground 25 feet. The distance, cap s , that the acorn is from the ground as it falls is represented by the equation cap s times t is equal to negative 16 t squared plus 25 , where t is the number of seconds. For which interval of time is the acorn moving through the air?
Answer
A
0 is less than t comma t is less than 5 fourths
B
negative 5 fourths is less than t comma t is less than 5 fourths
C
t is greater than 5 fourths
D
0 is less than t comma t is less than or equal to 5 fourths
Explanation
The acorn reaches the ground when its height is 0. Set −16t² + 25 = 0, so t² = 25/16 and the positive time is t = 5/4 seconds. It is moving through the air after it leaves the branch at t = 0 and before it hits the ground at t = 5/4, so the interval is 0 < t < 5/4 seconds: choice B.
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