The height hm of a firework rocket above the ground after t seconds is given by h= 35t-5t^2. Show that when the rocket is 50 m above the ground t^2-7t+10=0. Solve for t to find when the rocket is 50 m above the ground. When does the rocket land?
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Given is
h
(
t
)
=
−
16
t
2
+
160
t
It has not been explicitly given but it is presumed that
h
is the height of rocket and
t
is time in seconds.
Clearly the rocket will be in air between the time interval from
t
0
=
0
and
t
=
t
1
when height of the rocket is zero.
Setting the height
h
(
t
)
=
0
and solving for
t
−
16
t
2
+
160
t
=
0
Factorizing we obtain
−
16
t
(
t
−
10
)
=
0
We have two values of
t
from first factor
t
=
0
from second factor
(
t
−
10
)
=
0
⇒
t
=
10
We obtain
t
1
−
t
0
=
10
seconds is time for which the rocket is in the air.
Graphically
graph{y=-16x^2+160x [-5, 15,-15, 428]}
height
h
is plotted as
y
and time
t
as
x
We obtain time of flight as t = 10
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