## 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.

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Math
2 weeks
2021-09-11T19:00:52+00:00
2021-09-11T19:00:52+00:00 1 Answer
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## Answers ( )

Answer: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

]

.

tbh google