Answer:
2.687 seconds
Step-by-step explanation:
You want to know how long it takes a ball to hit the ground if its height is given by h = -16t² -24t +180.
Time
The ball will hit the ground when the height is zero:
0 = -16t² -24t +180
0 = t² +1.5t -11.25 . . . . . . divide by -16
0 = (t +.75)² -11.8125 . . . . complete the square
t +0.75 = √11.8125 . . . . . add 11.8125 and take the square root
t = -0.75 +√11.8125 ≈ 2.68693
The ball will hit the ground about 2.687 seconds after it is thrown.
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Additional comment
Only the positive answer is relevant in this problem.
