A toy rocket launched vertically into the air has position function s(t)= 64sqrt(t)-8t^2, where s=0 is the ground, s is measured in meters and t>0 is measured in seconds.
(a) How many seconds does the rocket spend traveling upward?
(b) After how many seconds does the rocket return to the ground?
(c) What is the maximum height reached by the rocket?
I have the answer sheet so I'm asking to show how you get the answer, thank you in advance!
(a) How many seconds does the rocket spend traveling upward?
(b) After how many seconds does the rocket return to the ground?
(c) What is the maximum height reached by the rocket?
I have the answer sheet so I'm asking to show how you get the answer, thank you in advance!
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s(t) = 64√t - 8t²
a)
s(t) = 64√t - 8t²
s'(t) = 32/√t - 16t = 0
t = ∛4
t ≈ 1.59 s
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b)
s(t) = 64√t - 8t² = 0
64√t = 8t²
8√t = t²
64t = t⁴
t⁴ - 64t = 0
t(t³ - 64) = 0
t = 0, t = ∛64
t = 4 s
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c)
max height t = ∛4
s(t) = 64√t - 8t²
s(∛4) = 64√t - 8t² = 48∛2 s
`````````````` `````````````````````≈ 60.48 m
a)
s(t) = 64√t - 8t²
s'(t) = 32/√t - 16t = 0
t = ∛4
t ≈ 1.59 s
`````````````
b)
s(t) = 64√t - 8t² = 0
64√t = 8t²
8√t = t²
64t = t⁴
t⁴ - 64t = 0
t(t³ - 64) = 0
t = 0, t = ∛64
t = 4 s
````````
c)
max height t = ∛4
s(t) = 64√t - 8t²
s(∛4) = 64√t - 8t² = 48∛2 s
`````````````` `````````````````````≈ 60.48 m