Kristin and her friends were playing around after basketball practice one day. Kristin decided to try a trick shot by standing on a 3 foot tall stool and tossing the basketball to the goal. Unfortunately, she missed and the path her ball took is shown in the graph below with height in feet and time in seconds. At what time did the basketball hit the ground?
Question 17 options:
6.5 seconds
-0.5 and 6 seconds
12 seconds
3 seconds
Answers
Given : try a trick shot by standing on a 3 foot tall stool and tossing the basketball to the goal.
To Find : At what time did the basketball hit the ground
Solution:
From the graph ball hit the ground between 6 and 7 secs
Hence 6.5 secs is the correct option
To find exact time
graph equation is
y = -x² + 6x + 3
y = 0
=> -x² + 6x + 3 = 0
=> x² - 6x - 3 = 0
=> (x - 3)² - 9 - 3 = 0
=> (x - 3)² = 12
=> x- 3 = ±2√3
=> x = 3 + 2√3 or -3 - 2√3
Negative time is not possible hence
x = 3 + 2√3
x = 6.464
around 6.464 secs basketball hit the ground
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