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Answer:
(a) 0.625 seconds (rounds to 0.63)
(b) 2.27 seconds
(c) No
Step-by-step explanation:
(a) We want to find t such that h = 60
60 = -16t^2 +10t +60
0 = t(-16t +10) . . . . . . . . . subtract 60, factor
t = 0 or t = 10/16 = 5/8 = 0.625
The stone is again 60 feet above the water after 0.625 seconds.
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(b) We want to find t such that h = 0
0 = -16t^2 +10t +60
16t^2 -10t = 60
16(t^2 -5/8t +25/256) = 60 +25/16 . . . . complete the square
(t -5/16)^2 = 61.5625/16 = 3.84765625 . . . . simplify a bit
t = 5/16 +√3.84765625 ≈ 2.274 . . . . square root, add 5/16
The stone strikes the water at about 2.27 seconds.
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(c) The equation above tells us the peak height of the stone is about 61.56 feet. It does not reach a height of 90 feet.
