## A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation ℎ() =

Question

A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation ℎ() = −162 + 64, where is the time in seconds. Determine the domain, using interval notation, for this function in the given context.

in progress 0
2 weeks 2021-09-11T19:00:52+00:00 1 Answer 0

Although strictly speaking of mathematics i.e. theoritically,

t

can take any value from

{

,

]
,

however, it is essentially a physical problem related to Physics and we cannot have negative

t  i.e.  t

0

Further, after the maximum is reached at  t
=
2  (observe that first differential is  h

(
t
)
=

32
t
+
64
, which is zero at  t
=
2  and second derivative  h

(
t
)
=

32  is negative and at this we have  h
(
2
)
=
64
), at  t
=
4
,  h
(
4
)
=
0  i.e. toy rocket falls back to the ground and as such, we cannot have  h
>
4
.

Hence, domain for  t  is  [
0
,
4
]
.