Problem 6
6. The formula for the height of a ball thrown straight up in the
air is
h(t) = -16t2 + 60t + 8
- a) Find h'(t) and h"(t).
- b) When is h'(t) = 0?
- c) When is h(t) = 8?
a) We need to find h'(t) and h"(t)
h'(t) = -32t + 60
h"(t) = -32
b) h'(t) = -32t + 60 = 0
when
-32t = - 60
or
t = (-60)/(-32)
= 15/8
c) h(t) = -16t2 + 60t + 8 = 8
when
-16t2 + 60t = 0
Factor
t(-16t + 60) = 0
Set the factors = 0
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t = 0
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-16t + 60 = 0
-16t = -60
t = (-60)/(-16)
= 15/4
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